Just googled it, and it looks like he did is a little differently. He paired 1 with n and then 2 with n-1, etc... yielding n/2 pairs that add up to n+1. It still works out to (n+1) * n/2, though :)

Apparently biographers disagreed about his age at the time but they all had the same method and the same problem of summing numbers from 1 to 100.