Chapter 8, Problem 7RE

(a)

To determine

To prove: $1^k+2^k+\mathrm{....}+n^k=O\left(n^{k+1}\right)$ for any $k\ge 1$.

(b)

To determine

To prove: $1^2+2^2+\mathrm{....}+n^2\approx n^3$.