Question

The value of $\displaystyle\lim_{n\to\infty} \left[\frac{n}{n^{2}+1^{2}}+\frac{n}{n^{2}+2^{2}}+\ldots+\frac{1}{n^{2}+2n}\right]$ is

• A. $\frac{\pi}{4}$
• B. $\log \, 2$
• C. $0$
• D. $1$

Answer 1

Answer: (A)

$\frac{\pi}{4}$

Answer 2

$\displaystyle\lim_{n\to\infty} \left[\frac{n}{n^{2}+1^{2}}+\frac{n}{n^{2}+2^{2}}+\ldots+\frac{n}{n^{2}+n^{2}}\right]$