error in the approximation sigma 1/(n^2) from 1 to infinity =~ sigma 1/(n^2) from 1 to 1000?

Question

Assume that we want to find the sum s of the series 1/(n^2) from 1 to infinity approximately, and we estimate s is approximately equals to the sum of the series 1/(n^2) from 1 to 1000.
Find an upper bound for the error in the above approximation.

Answer 1

Since the series converges, the next term in the series, 1/(1001)^2 is an upper bound.