\lim_{n\rightarrow \infty}\left [ \frac{1}{n} + \frac{n^{2}}{(n+1)^{3}}+ \frac{n^{2}}{(n+2)^{3}} +...+\frac{1}{8n}\right ]=

  • Option 1)

    \frac{3}{8}

  • Option 2)

    0

  • Option 3)

    \frac{1}{4}

  • Option 4)

    \frac{1}{5}

 

Answers (1)

 

Walli's Method -

Definite integral by first principle

\int_{a}^{b}f(x)dx= \left ( b-a \right )\lim_{n \to \infty }\frac{1}{n}\left [ f(a) +f(a+h)+f(a+2h)....\right ]

where

h=\frac{b-a}{n}

- wherein