To prove that the sum of 1/n^2 from n=1 to 100 is less than 2, we can calculate the sum directly:

1 + 1/2^2 + 1/3^2 + ... + 1/100^2 = 1 + 1/4 + 1/9 + ... + 1/10000

This sum can be approximated by using the integral test for convergence. The integral of 1/x^2 from 1 to infinity is -1/x evaluated from 1 to infinity, which equals 1. This means that the sum of 1/n^2 from n=1 to infinity is convergent.

Since the sum of 1/n^2 from n=1 to 100 is a finite sum and less than the sum from n=1 to infinity, we can conclude that the sum of 1/n^2 from n=1 to 100 is less than 2.