$\underset{x→∞}{\lim}\frac{1}{n}\left(1+\sqrt{\frac{n}{n+1}}+\sqrt{\frac{n}{n+2}}+.....+\sqrt{\frac{n}{4n-3}}\right)$ is equal to

1 2 3 none of these

2

Given limit $\underset{x→∞}{\lim}\frac{1}{n}\left(1+\sqrt{\frac{n}{n+1}}+\sqrt{\frac{n}{n+2}}+.....+\sqrt{\frac{n}{4n-3}}\right) = \int\limits_{0}^{3}\frac{dx}{\sqrt{1+x}}=2\sqrt{1+x}|_{0}^{3}=2$