Question

$\lim_{n \rightarrow \infty}$ $\frac { 1 } { \mathrm { n } }$ $\sum_{r = 1}^{n}\frac{r}{\sqrt{n^{2} + r^{2}}}$ is equal to -

• A. 1 – $\sqrt{2}$
• B. $\sqrt{2}$ – 1
• C. $\sqrt{2}$
• D. – $\sqrt{2}$

Answer 1

Answer: (B)

$\sqrt{2}$ – 1

Answer 2

$\lim_{n \rightarrow \alpha}$1/n$\sum_{r = 1}^{n}{r/n\sqrt{1 + (r/n)^{2}}}$\ $\int_{0}^{1}{x/\sqrt{1 + x^{2}}dx}$ Ž 1 + x² = t²

Ž xdx=tdt \$\int_{1}^{\sqrt{2}}{tdt/t}$Ž=$\sqrt{2}$– 1