Prove that the ff. sequence are null.

Question

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*}

Answer 1

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 $x$.