IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

oneyeartogo

$\mathop{\lim}\limits_{{n} \to {\infty}} \frac{1}{n} \Sigma\;\frac{r}{\sqrt{( r^2 + n^2}}$

Note: Summation is from r = 1 to r = 2n (How do I add it to the equation?)

The answer given is $- 1 + \sqrt{5}$

Please give the method

feynmann

It is from Fundamental theorem of integral calculus

put r/n = x , 1/n =dx

so it is $\int_{0}^{2} x/\sqrt{1+}{x}^{2} dx$ It can be easily evaluated .

oneyeartogo

Is there another way to do it as I don't know much abt Integration?