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\text { Evaluate }       {\lim _{n \rightarrow \infty}\left(\frac{1}{n^2}+\frac{2}{n^2}+\frac{3}{n^2}+\cdots+\frac{n}{n^2}\right)}

Option: 1

1/2


Option: 2

3/4


Option: 3

5/6


Option: 4

0


Answers (1)

best_answer

\text { With integrals: }

{\lim _{n \rightarrow \infty}\left(\frac{1}{n^2}+\frac{2}{n^2}+\frac{3}{n^2}+\cdots+\frac{n}{n^2}\right)=\lim _{n \rightarrow \infty} \frac{1}{n}\left(\frac{1}{n}+\frac{2}{n}+\frac{3}{n}+\cdots+\frac{n}{n}\right)=\int_0^1 x d x=\frac{1}{2} .}

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Rishi

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