# Math Help - Big O

1. ## Big O

Let $N > M$. Prove that for $k > 1$, $\sum_{n=M+1}^{N} n^{-k} = O(M^{-k+1})$ as $M \to \infty$.

2. Observe your sum is bounded above by the integral of 1 \x^k from M to N-1, which you can easily evaluate directly obtaining two terms bounded by C/M^(k-1) as needed.