Find the sum of the first 500 positive integers.

thanks for any help!

There is a story about the famous German mathematician Gauss who, while in primary school,was given that problem by his teacher in an effort to occupy the pupils by making them add a list of integers. The young Gauss reputedly produced the correct answer within seconds, to the astonishment of his teacher. Gauss's presumed method, which had the list of numbers was from 1 to 500, was to notice that the first plus the last was 501, the second plus the secondlast was 501 etc.

and he noticed that he could form 250 such pairs.
a quick calculation of 501 x 250 gave him 125250

To find the sum of the first 500 positive integers, you can use the formula for the sum of an arithmetic series. The formula is:

sum = (n/2) * (first term + last term)

In this case, the first term is 1, because we are finding the sum of the first positive integers. The last term is 500.

Plugging in the values into the formula, we get:

sum = (500/2) * (1 + 500)
= (250) * (501)
= 125,250

So, the sum of the first 500 positive integers is 125,250.

That's very cool! Thank you for your time!

I enjoyed that story!

There is also the formula
1 + 2 + ... + n = n(n+1)/2
= (500)(501)/2

Reiny's explanation is a neat way of remembering it (when n is even): n/2 pairs, each with a sum of n+1. It also works for n odd, but that is not as obvious