Question

Find the limit

\[\lim_{n \rightarrow \infty} \frac{ 1 }{ n } \sum_{i=1}^{n} \frac{ 1 }{ 1+(\frac{ i }{ n })^2 }\]

Answer 1

I got:

\[\frac{ \pi }{ 4 }\]

Answer 2

Is that right?

Answer 3

\[\lim_{n \rightarrow \infty} \frac{ 1 }{ n } \sum_{i=1}^{n} \frac{ 1 }{ 1+(\frac{ i }{ n })^2 }\]

Answer 4

yes you are right .. change it into integration

Answer 5

Thanks :) .

Answer 6

this should be equal to
\[ \int_0^1 {1 \over 1 + x^2} dx\]