# Let's do some calculus! (34)

Calculus Level 5

Find the value of the positive constant $$c_0$$ such that the series given below

$\displaystyle \sum_{n=0}^{\infty} \dfrac{n!}{{(cn)}^n}$

diverges for $$0 < c < c_0$$ and converges for $$c > c_0$$.

Clarification: $$e \approx 2.71828$$ denotes the Euler's number.