how to calculate the first hundred terms of a sequence​

Answers

Answer 1

Answer:

Question: what is the sum of the first 100 whole numbers?? how am i supposed to work this out efficiently? thanks

The question you asked relates back to a famous mathematician, Gauss. In elementary school in the late 1700’s, Gauss was asked to find the sum of the numbers from 1 to 100. The question was assigned as “busy work” by the teacher, but Gauss found the answer rather quickly by discovering a pattern. His observation was as follows:

1 + 2 + 3 + 4 + … + 98 + 99 + 100

Gauss noticed that if he was to split the numbers into two groups (1 to 50 and 51 to 100), he could add them together vertically to get a sum of 101.

1 + 2 + 3 + 4 + 5 + … + 48 + 49 + 50

100 + 99 + 98 + 97 + 96 + … + 53 + 52 + 51

1 + 100 = 101

2 + 99 = 101

3 + 98 = 101

.

.

.

48 + 53 = 101

49 + 52 = 101

50 + 51 = 101

Gauss realized then that his final total would be 50(101) = 5050.

The sequence of numbers (1, 2, 3, … , 100) is arithmetic and when we are looking for the sum of a sequence, we call it a series. Thanks to Gauss, there is a special formula we can use to find the sum of a series:

S is the sum of the series and n is the number of terms in the series, in this case, 100.

Hope this helps!


Related Questions

Which of these organisms is a vertebrate?

Answers

Answer:

vertebrate, animals with a backbone, and invertebrate, animals without a backbone

Explanation:

A. worm - no because a worm has no back bone

B- Chimpanzee- Yes because they have a backbone

C. Bacterium- no because it is a bacteria

D. Grass- no because no backbone

so ur answer is b

Answer:

B. Chimpanzee

Explanation:

A chimpanzee is a vertebrate, not an invertebrate.

Which part of the brain controls body movements and processes information from the sense organs? (1 point)

Answers

Answer:

cerebral cortex

Explanation:

I'm pretty sure that is correct

The "splitting apart" of cells is called :

options:

cell fissions
cell division

Answers

Answer:

 all

Cell division is the process by which a parent cell divides into two or more daughter cells :3

hope this helps :)

cell division.......

Which of the following is NOT part of the definition of intelligence?
A) Ability to adapt
B) Ability to think and reason clearly
C) Ability to be creative
D) To act purposefully

Answers

probably d) but im not 100% sure

Which tree above shows a different evolutionary history from the others? Explain your answer.[ ]

Answers

Answer:

the second one is the right answer

The second evolutionary tree (2) is showing a different evolutionary history from the other trees.

What is an evolutionary tree?

An evolutionary tree is a diagram/graphic used in biology to show evolutionary relationships between taxa.

The taxa located at the tree can be different species, genera, orders, etc.

An evolutionary tree is monophyletic when all descendants originated from the same ancestor.

In conclusion, the second evolutionary tree is showing a different evolutionary history from the other trees.

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Which topic do biologists ask questions about and study using the scientific
process?
O A. Organisms and health
O B. Computer technology
Ο Ο Ο Ο
O C. Philosophy and art
D. Government elections

Answers

Answer:

By using, the scientific method Biology is capable of studying the different components of the organisms, including the Genes, Bacterias, and viruses, making Health one of the main subjects of study for the Biologists.

soo in my thought

A. Organisms & heath

B sjdjfjjfjfjdjdjfjjdifitjtjtitjjtjrut

5. Gas stations aren't just places to fill up the tank. Can you find 2 things that Shaq at
the Recycle City gas station does to help the environment?

Answers

Answer:

decrease pollution also make the air fresher

Explanation:

I know this because instead of burning trash they reuse it .

The photograph shows one way individuals work together in groups. What
kind of work is shown in the photograph?
2
A. Postindustrial work
B. Gathering resources
c. Agricultural work
OO
D. Domesticating animals

Answers

i think the answer would be. B

A population of prairie dogs shares a habitat with a population of bison. The
bison migrate to another area. How will the prairie dog population size
change?
A. It will decrease to zero.
B. It will remain approximately the same.
C. It will increase.
D. It will decrease slightly.

Answers

C. It will increase

When does an infection become a disease?​

Answers

Answer:

Infection occurs when viruses, bacteria, or other microbes enter your body and begin to multiply.

Explanation:

Infection occurs when viruses, bacteria, or other microbes enter your body and begin to multiply. Disease, which typically happens in a small proportion of infected people, occurs when the cells in your body are damaged as a result of infection, and signs and symptoms of an illness appear.

Consider a simple food web. Assume that the grass 1000 Kcal of energy. Using your understanding of energy transfer, evaluate each of the statements provided choose all that are correct.

A) There is 100 Kcal available to the snake
B) There is 1 Kcal of energy available to the hawk
C) There is 10 Kcal available to the shrew
D) There is 100 Kcal available to the rabbit
E) There is 900 Kcal available to the grasshopper

* Select all that apply *

Answers

Evaluating each of the statements provided about energy flow in a food web, the correct statements are:

B) There is 1 Kcal of energy available to the hawkC) There is 10 Kcal available to the shrewD) There is 100 Kcal available to the rabbit

What is the flow of energy in a food web?

The flow of energy in a food web is the transfer of energy from one organism to another as they consume and are consumed by other organisms.

The energy flow in a food web typically starts with primary producers, such as plants, algae, and some bacteria, which convert sunlight or chemical energy into organic matter through photosynthesis or chemosynthesis.

For every higher level, only 10% of the energy of the lower level is transferred.

Learn more about a food web at: https://brainly.com/question/4656320

#SPJ1

what are the male se.x accessory ducts​

Answers

Answer:

Male accessory sex glands include the seminal vesicles, prostate, and bulbourethral glands. The secretion from each of these glands is added to the testicular fluid and forms a substantial part of the semen. The seminal vesicles are elongated, saclike structures that lie posterior to the prostate gland.

; ) Have a great day

Which of the following is not associated with a tRNA molecule?
anti-codon
amino acid
transcription
translation

Answers

Answer:

transcription or translation

Explanation:

well we can eliminate amino acid immediately and and anti-condon I would go for transcription but it could be translation

student use a microscope to look for structures present in 4 different cells. The students place in X for each structure that was viewed for each cell on the table shown



which cell that was viewed is more most likely prokaryote


please help

I would give brainliest and 5 stars and 10 points for the best answer

if I see a link as they answer you will be reported

Answers

Answer:

Cell X

Explanation:

Prokaryotes do not have a nucleus or chloroplasts.

g The stationary phase in gas chromatography is best described as: is a column packed with solid particles that that come in contact with a liquid mobile phase is a thin liquid layer that is chemically bonded to the interior of a capillary column that comes in contact with an inert carrier gas or mobile phase is the interior surface of a untreated capillary column that comes in contact with a liquid mobile phase passing through the column a thin layer of silica or alumina particles bound to a two dimensional plate

Answers

Answer:

Hello your question is poorly written, the options and the question is all mixed up but i was able to pick out the correct answer.

answer : A thin liquid layer that is chemically bonded to the interior of a capillary column that comes in contact with an inert carrier gas or mobile phase

Explanation:

The stationary phase in gas Chromatography is best described as ( from the options listed in your question ) :

A thin liquid layer that is chemically bonded to the interior of a capillary column that comes in contact with an inert carrier gas or mobile phase

Gas chromatography is an analytical process  used to separate the chemical components ( usually gases )  found in a mixture sample  

What are advantageous traits more likely to be passed onto offspring of the following statements is an

Answers

Answer:

Why are advantageous traits more likely to be passed onto offspring? Because they are more likely to survive and reproduce. Because they come from dominant alleles. Because they come from recessive alleles.

Explanation:

i know its alot but i just want you to get the right answer

explain the characteristics scientists use when observing organisms and placing them in six kingdoms

Answers

“Classification of organisms is done while considering many factors such as:
Cell type- whether the organism is prokaryotic or eukaryotic
Cell structure- This includes both the presence and composition of the cell wall
Body type- whether the organism is multicellular or unicellular
Mode of nutrition- the method through which the organism achieves its nutritional requirement, by consuming other organisms (heterotroph) or making its own food (autotroph)”.

Which of the following does not influence demography?
fertility rates
growth rates
archaeology finds
factors that increase death rates

Answers

archaeogy finds. its the only thing that doesnt affect people and populatoin

Which of the following is an example of a simple endocrine
pathway?
a. prouth regulation be the producten nach harmone
meta con bure thyr
c. release of secrein by endere cels in duodenum due to low, pH
d. antidiuretic romane secretion de rosterior prutar in response to blood osmolaly​

Answers

Answer:

get help

Explanation:

get helpjsjsjjjjsjjjjsjjsjshanasnsddjdjsjs

Choose the one that protects the investor."
the FBI
the SEC
the police
the NFL

Answers

SEC or better said Securities and Exchange Commission

Place a single word into each sentence to make it correct, then place each sentence into a logical paragraph order. Blood leaving the chambers Waste products will then be ____________ by the tubules.

Answers

Answer:

Blood goes to lungs for the removal of carbondioxide and loading of oxygen whereas kidney filters the blood and sent the waste to urinary bladder.

Explanation:

Blood leaving the chambers and this blood goes to the lungs through pulmonary artery that carries deoxygenated blood. In the lungs, carbondioxide gas is removed from this blood and oxygen is added to the blood. This oxygenated blood goes to the heart through pulmonary vein and the heart pump this blood to all parts of the body. Waste products that is produced during metabolism in the liver will then be transported to the kidney for filtration by the tubules. After filtration the waste products are sent to the urinary bladder through ureters.

Which is NOT an example of a characteristic you might use to classify a bird?
beak size and color
feather colors
year of its birth
leg type

Answers

Answer:

year of its birth

The answer is : Year of birth. You can not tell what a bird is by when it’s born.

"ucture and properties of Matter

Question 1 of 20

Which statement describes the difference between covalent bonds and Van

der Waals forces?

O A. Covalent bonds form from the attraction of positive ions and

freely moving electrons, while Van der Waals forces cause an

attraction between nonpolar molecules.

B. Covalent bonds form when there is an attraction between

nonpolar molecules, while Van der Waals forces cause two atoms

to share valence electrons.

C. Covalent bonds occur when two atoms share valence electrons,

while Van der Waals forces cause an attraction between positive

Answers

Answer:

Covalent bonds form when two atoms share valence electrons,

while Van der Waals forces cause an attraction between nonpolar

molecules

Explanation:

A covalent bond is said to be formed when two atoms of the same or different elements share electrons. In an ordinary covalent bond, each bonding atom contributes one valence electron while in a dative covalent bond only one of the bonding atoms provides the shared pair of electrons.

Van Der Waals forces is the major intermolecular interaction between non polar compounds. Van Der Waals forces " are caused by correlations in the fluctuating polarizations of nearby particles"(Wikipedia).

Answer:

Covalent bonds form when two atoms share valence electrons, while Van der Waals forces cause an attraction between nonpolar molecules.

Explanation:

Apex.

i need help with this please

Answers

Answer:

1st Activity = Cold Front

2nd= High Pressure with a Cold Front

How can poor nutrition lead to a change in trait expression?

Answers

Answer: Poor nutrition won't provide healthy amounts of energy to the body.  The lack of nutritional vitamins that the body needs can lead to a change in hormonal signals, stimuli, and metabolites.

Hope this helps :)

In the overall health management, nutrition plays a very recognizable function, however, the role of genetics in nutritional impact is yet to be understood completely.  

Genetic variability in relation to nutrition may be partly accountable for differences among the individuals in metabolism, absorption of food, enzyme digestion, excretion, storage, and others.  

Nutrigenetics and nutrigenomics are the two areas of study regarding genetics and nutrition that looks for the effect of genetic variations on dietary responses, and the function nutrients perform in bioactive food compounds and expression of the gene.  

• The three prime factors in nutrigenomics and nutrigenetics are ethnic diversity, malnutrition, and availability of food.  

• In the existence of chronic malnutrition, the genomic stability and gene expression can be influenced, with genome stability sometimes resulting in mutations of gene sequences and mutations at the levels of chromosomes.  

Thus, poor nutrition can result in the change in the expression of trait.

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How would altering the ph of an ecosystem affect the organisms that live there? Relate to enzyme function.
In your response include why slight changes in pH are significant to living things.

Answers

Answer:

pH: Each enzyme has an optimum pH range. Changing the pH outside of this range will slow enzyme activity. Extreme pH values can cause enzymes to denature. Enzyme concentration: Increasing enzyme concentration will speed up the reaction, as long as there is substrate available to bind to.

Hope this helps and if this is wrong sorry!!!

What determines the direction of gas movement?

Answers

Answer:  The direction of gas movement is determined by partial pressure differences. 2) At the arterial end of the pulmonary capillaries, O2 diffuses from the alveoli into the blood, while CO2 diffuses from the blood into the alveoli.

Explanation:

→ Oxygen and carbon dioxide diffuse across a respiratory membrane.

Factors determining gas movement:

The concentration gradient of the gases and the partial pressure of the gases.The differences in concentration on either side of the cell membrane.

In diffusion of gases:

The amount of surface area available for diffusion.The distance the gas particles must travel.The higher the concentration gradient across the gas-exchanging surface, the faster the rate of diffusion across it.

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2. What does the atomic model teach you about the ability of scientists to
study things that cannot be directly observed?

Answers

Answer:

The atomic model is our understanding of how the atom is structured. At one point in history, people believed that any substance was simply made of that substance and would retain that property no matter how small a quantity it was reduced to. Later, some argued that all matter was made of tiny particles called atoms. While this is correct, later researchers found that even the atoms were made of smaller particles called electron, protons, and neutrons. More recently, scientists have discovered quarks, tiny particles that makeup protons and neutrons.

HURRY DUE TODAY
Which of the following are specialized stem structures?
Group of answer choices

pistils, stamens, anthers

xylem, phloem, ray cells

corms, tubers, bulbs, stolons, rhizomes

epidermis, mesophyll, palisade layers

Answers

Answer:

d

Explanation:

Which of the following describes the benefits of thinning a stand as a means of limiting disease?
O It gives weaker trees a better chance.
O It allows healthy trees to become stronger.
O The removed trees can be used for lumber.
O Most pests will not travel form one tree to another.
Mark this and return
Next
Submit

Answers

Answer:

I think it is it gives weaker trees a better chance

Explanation:

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