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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

As it sounds pretty much like homework you will just get a hint:

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

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