# Thread: state whether the sequence converges

1. ## state whether the sequence converges

as n --> infinity, if it does, find the limit

$ln(n+1)/n$ I know that $ln n/n --> 0$

$x^{100n}/n!$ I know that $x^n/n! --> 0$

2. Originally Posted by wopashui
as n --> infinity, if it does, find the limit

$ln(n+1)/n$ I know that $ln n/n --> 0$
Use L'Hospital's Rule.

$x^{100n}/n!$ I know that $x^n/n! --> 0$
Test the convergence of $\sum \frac{x^{100n}}{n!}$. you should know that if $\sum a_n$ converges, then $a_n \rightarrow 0 \,\ as \,\ n\rightarrow\infty$.
Ratio test is the best choice for this one.
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3. Originally Posted by Miss
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we have not cover the Ratio test , can we just use the property of limit of sequence to slove it?