Originally Posted by

**Shakarri** I was asked to prove that $\displaystyle \frac{c^n}{n!}$ is a null sequence, that is, $\displaystyle lim_{n->\infty}\frac{c^n}{n!}=0$. c is a real number.

I said that the sequence tends to zero if for all n sufficiently large the denominator grows faster than the numerator. If this is true for all n sufficiently large then the denominator is infinitely larger than the numerator in the limit and so the limit is zero.

The numerator grows at the rate $\displaystyle \frac{c^{n+1}}{c^n}=c$ and the denominator grows at the rate $\displaystyle \frac{(n+1)!}{n!}=n+1$

For any c there exists n_{0} such that n+1>c for all n>n_{0} therefore the sequence is a null sequence.

I got zero marks for this, the lecturer later gave the solution in the image I attached. Maybe he was just being picky but I don't see what is wrong with my proof, could someone please show me where I went wrong if I went wrong?