Hi, I am having a bit of trouble with this 'show that' question.

So question asks you to show:
$\displaystyle | \frac{1}{E_2(x)}-g_n(x)| \le \frac{|x|^n e^{|x|}}{(n+1)!}$

where $\displaystyle E_2(x) = \frac{x}{e^x-1}$ when it doesn't equal to 0 and 1 when it equals to zero. And $\displaystyle g_n(x)= \sum^n_{k=1} \frac{x^{k-1}}{k!}$.

Where should I start off and how so? If someone can show me, it will be highly appreciated.

Should I be expanding the series out? Or do i have to notice something about the RHS?