Question

evaluate limx-0(n/1+n^2+n/4+n^2+n/9+n^2+.....+n/2n^2)

Answer 1

$lim_{n\rightarrow0}(\dfrac{n}{1+n^2}+\dfrac{n}{4+n^2}+\dfrac{n}{9+n^2}+.....+\dfrac{n}{2n^2})$

The value of all the terms in given limit is 0 except last term

$\Rightarrow lim_{n\rightarrow 0}\dfrac{1}{2n}$

$=\dfrac{1}{0}=\infty$

Hence The given limit does not exist.