# Upper bound of $nc^n$

Is it true that $$nc^n \leq (c+1)^n$$, where $$c$$ is a constant? If so, how?

• Try induction to prove your inequality.
– Jut
Sep 3 '21 at 19:11

It comes from $$\left(\frac{c}{c+1}\right)^n\cdot n \to 0$$ when $$n\to \infty$$.