What do you get by adding all the numbers from 1 to 200? To answer this question think about these questions first:

a. What is the sum of the first number and the last number?

b. What is the sum of the second number and the second to last number?

c. What is the sum of the third and the third to the last number?

d. If you pair up all the numbers as suggested above, how much does each pair add to and how many pairs are there?

Now you should be able to answer the original question.

Guest Jul 2, 2018

#1**+2 **

\(1+2+3+\cdots+198+199+200=?\)

a.

First number: 1,

Last number 200.

\(1+200=\boxed{201}\)

b.

Second number: 2,

Second to last number: 199.

\(2+199=\boxed{201}\)

c.

Third number: 3,

Third to last number: 198.

\(3+198=\boxed{201}\)

d.

When you pair up all the numbers as suggested above, each pair adds to 201.

Since there are 2 numbers in each pair, and there are 200 numbers, there are 200 ÷ 2 = 100 pairs.

e.

Since each pair sums to 201, and there are 100 pairs, \(1+2+3+\cdots+198+199+200=201\cdot100=\boxed{20100}\)

GYanggg
Jul 2, 2018

#2**+1 **

This is easy. The formula for the sum of a set of consecutive numbers is, when starting from one, (1+n)n/2. Here n equals 200. 200*201/2=100*201=20100

kevbamboo
Jul 2, 2018

#3**+2 **

Yes, kevbamboo, I well understand that there are multiple ways of approaching this problem.

Your way completely skips steps a, b, c, and d.

If you want to get technical, I can use 4 different methods to calculate the sum, and start my solution off with "this is easy".

However, the method the questioner requests is obviously the one presented in my solution.

Steps a, b, c, and d are just parts of the proof and investigation of the method.

GYanggg
Jul 2, 2018

#4**-2 **

It’s irritating when a BAMBOOzler comes in all cocky and full of himself, and says, “This is easy,” after you painstakingly answer the question. It is less irritating though than saying, “I hope this helped,” at the end of almost every post.

**I hope this helped. **

Guest Jul 2, 2018

#5**+3 **

However, the most irritating of all, are guests who hide behind their anonymity and spew **BS** that absolutely does not help the growth of the questioner.

Saying "I hope this helped" is just simply a positive signature of mine, concluding my solution, much better than starting your answer off with "this is easy". I think this, we can both agree on.

So, Guest, instead of taking your time to write these futile responses, please go learn some math, or how to use the comma, or something else that will contribute to the overall mentality of the user of this website.

I hope this helped,

Gavin.

GYanggg
Jul 2, 2018

#6**-1 **

**My, my! Aren’t we a little pissy this week? **

I think irritating the questioners and everyone else who reads your posts, with your *positive signature ***doesn’t** help the growth of the questioner, or anyone else. I agree that anonymous guests that spew BS are irritating, but only slightly more so than members that spew BS.

*Saying "I hope this helped" is just simply a positive signature of mine, concluding my solution, much better than starting your answer off with "this is easy". I think this, we can both agree on. *

I think we both CAN’T agree on that. You present as arrogant with a false sense of humility. Starting with “This is easy,” is a preposition indicating the math is not difficult to do or learn. It may seem arrogant, but there is certainly no false humility in it.

*So, Guest, instead of taking your time to write these futile responses, please go learn some math, or how to use the comma, or something else that will contribute to the overall mentality of the user of this website. *

My response isn’t futile. While I could always learn more mathematics, my skills are at least four levels above yours, so I don’t learn much from your posts. That is from your regular posts. You have a few posts that jump several levels above your norm, indicating close supervision from a well-educated governor/governess. This isn’t a criticism. I think they are great.

I suppose I could learn how to use a comma better, but coming from you this is amusing. Your punctuation needs improvement. However, your English syntax is very good. It’s better than most of the adults on this forum.

Does this post *contribute to the overall mentality of the user of this website? *

I think is does.

**I hope this helped.**

Guest Jul 2, 2018