$\lim _{n \rightarrow \infty} \frac{1}{n^3} \sum_{k=1}^n (k^2 x)$ ની કિંમત શોધો.

$\lim _{n \rightarrow \infty} \left[ \frac{n}{n^{2}+1^{2}} + \frac{n}{n^{2}+2^{2}} + \ldots + \frac{n}{n^{2}+n^{2}} \right]$ ની કિંમત શોધો.

$\lim _{n \rightarrow \infty}\left[\left(1+\frac{1}{n^3}\right)^{\frac{1}{n^3}}\left(1+\frac{8}{n^3}\right)^{\frac{4}{n^3}}\left(1+\frac{27}{n^3}\right)^{\frac{9}{n^3}} \ldots \left(1+\frac{n^3}{n^3}\right)^{\frac{n^2}{n^3}}\right]=$

$\mathop {\lim }\limits_{n \to \infty } \left[ {\frac{n}{{1 + {n^2}}} + \frac{n}{{4 + {n^2}}} + \frac{n}{{9 + {n^2}}} + .... + \frac{1}{{2n}}} \right]$ નું મૂલ્ય કેટલું થાય?

$\lim _{n \rightarrow \infty}\left(\frac{1}{\sqrt{n^2}}+\frac{1}{\sqrt{n^2-1}}+\ldots+\frac{1}{\sqrt{n^2-(n-1)^2}}\right)=$

$\lim _{n \rightarrow \infty}\left(\frac{1}{1+n}+\frac{1}{2+n}+\frac{1}{3+n}+\ldots+\frac{1}{2 n}\right)$ ની કિંમત શોધો :-