(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove [itex] \lim_{n\rightarrow\infty} \frac{p(n)}{e^n} = 0[/itex] where [itex] p(x) = a_k x^k + ... + a_1 x + a_0 [/itex] (with real coefficients [itex] a_i [/itex] in [itex] \mathbb{R} ) [/itex]

3. The attempt at a solution

I thought about using series to try and prove this, but I couldn't get it to work out and I think there is an easier way.

[itex] \frac{p(n)}{e^n} [/itex] = [itex] \frac{ \sum_{n=0}^\infty a_k n^k}{\sum_{n=0}^\infty \frac{n^k}{k!}} [/itex] = [itex] \frac{ \sum_{n=0}^\infty a_k}{\sum_{n=0}^\infty \frac{1}{k!}} [/itex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Formal limit proof

**Physics Forums | Science Articles, Homework Help, Discussion**