Question

Please anyone solve it.​

Answer 1

Answer:

0

Step-by-step explanation:

$\lim_{n \to \infty} (\frac{0}{n^2 +0^2} +\frac{1}{n^2 +1^2} +\frac{2}{n^2 +2^2} +.......+\frac{n}{n^2 +n^2} +..............+\frac{2n-1}{n^2 +(2n-1)^2}+\frac{2n}{n^2 +(2n)^2})$

=$\lim_{n \to \infty}( 0 +\frac{1}{n^2 +1} +\frac{2}{n^2 +4} +.......+\frac{n}{2n^2} +..............+\frac{2n-1}{5n^2 -4n+1}+\frac{2n}{5n^2 })$

=$\frac{1}{\infty}} +\frac{2}{\infty}} +.......+\lim_{n \to \infty}(\frac{n}{2n^2} +..............+\frac{2n-1}{5n^2 -4n+1}+\frac{2n}{5n^2 })$

= 0+ $\lim_{n \to \infty}(\frac{1}{4n} +..............+\frac{2}{10n -4}+\frac{2}{10n })$  (applying L/hospital rule)

= 0+ $(\frac{1}{\infty} +..............+\frac{2}{\infty}+\frac{2}{\infty })$

=0