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
Find the sum of the first 500 positive integers.
thanks for any help!
3 answers
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
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
1 answer