# Prove that the ff. sequence are null.

Prove that the ff. sequence are null. a. {1/n^2 +n} b. {(-1)^n /n!} c. {sin n^2 / n^2 +2n} d. { 1/ 3n^4 (2n-1)^1/3

A $\LaTeX$ interpretation of you sequence: \begin{align*} a_n &= \frac{1}{n^2+n}\\ b_n &= \frac{(-1)^n }{n!}\\ c_n&= \frac{\sin(n^2)}{n^2+2n}\\ d_n&=\frac{1}{3n^4 \sqrt[3]{2n-1}} \end{align*}

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Do you have any idea how to do any of these yourself? any idea where to start? Is there some particular place where you get stuck? Is there some reason for your being interested in these particular problems? –  Gerry Myerson Mar 2 '13 at 12:05
I set your sequences in $\LaTeX$ please check if I did it right, I added the homework tag, please remove it, when it is no homework –  Dominic Michaelis Mar 2 '13 at 12:12
@DominicMichaelis, Tnx for edit this post,It was very complicated. –  M.Sina Mar 2 '13 at 12:15

Use comparism with other sequence and use $|\sin(x)|\leq 1$ for all $x$.