Compute the following limit $\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{\sqrt{n^2+kn}}$
Please I need your help asap
Cheers
Matthew
Compute the following limit $\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{\sqrt{n^2+kn}}$
Please I need your help asap
Cheers
Matthew
$\sum_{k=1}^n\frac{1}{\sqrt{n^2+kn}}=\frac{1}{n}\sum_{k=1}^n\frac{1}{\sqrt{1+\frac{k}{n}}}\xrightarrow [n\to\infty]{}\int_0^1\frac{dx}{\sqrt{1+x}}$