Originally Posted by
wopashui as n --> infinity, if it does, find the limit
$\displaystyle ln(n+1)/n$ I know that $\displaystyle ln n/n --> 0$
Use L'Hospital's Rule.
$\displaystyle x^{100n}/n!$ I know that $\displaystyle x^n/n! --> 0$
Test the convergence of $\displaystyle \sum \frac{x^{100n}}{n!}$. you should know that if $\displaystyle \sum a_n$ converges, then $\displaystyle a_n \rightarrow 0 \,\ as \,\ n\rightarrow\infty$.
Ratio test is the best choice for this one.