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  • Calculating the limit of    <img alt="\lim _{n \rightarrow \infty}\left(\frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\ldots+\frac{1}{2 n}\right)" src="https://entrancecorner.oncodecogs.

Calculating the limit of    \lim _{n \rightarrow \infty}\left(\frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\ldots+\frac{1}{2 n}\right)

Option: 1

\ln 2


Option: 2

\quad \ln 3


Option: 3

\quad \ln 5


Option: 4

0


Answers (1)

best_answer


\sum_{n=k+1}^{2 k} \frac{1}{n}=\frac{1}{n} \sum_{n=1}^k \frac{1}{1+\frac{n}{k}}

which is related to this integral via a Riemann sum :

\int_1^2 \frac{1}{x} d x=\ln 2 .
 

Posted by

Ritika Harsh

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