Show that $1^k+2^k+...+n^k$ is $O (n^{k+1})$.

Question

Let $k$ be a positive integer. Show that $1^k+2^k+...+n^k$ is $O (n^{k+1})$.

So according to the definition of big-$O$ notation we have:

$$1^k+2^k...+n^k ≤ n(n^k) = n^{k+1}$$

whenever $n>1$

Is this a satisfied answer? can someone help?