Borwein and Borwein?

Calculus Level 2

True or false : $\large \sum_{n=1}^\infty \dfrac {\sin n}n = \sum_{n=1}^\infty \left(\dfrac {\sin n}n\right)^2$

True False

1 solution

Ritik Agrawal
Apr 15, 2017

Manipulate ln(1+x) series and convert it in the required form.. For sinn.. We can put x=e^i and use the property... The left hand side of the equation's Imaginary part is our answer.

What required form? What property?

Pi Han Goh - 4 years, 2 months ago

Sinx=(e^ix -e^-ix)/2i then opening the square bracket we can solve the individual series using ln(1+x) series

ritik agrawal - 4 years ago

Sinx=(e^ix -e^-ix)/2i then opening the square bracket we can solve the individual series using ln(1+x) series

ritik agrawal - 4 years ago

Can you elaborate more? I couldn't understand.

Shib Shankar Sikder - 10 months, 2 weeks ago

put sinx as e^i then take imaginary part of the final answer.

ritik agrawal - 9 months, 1 week ago

Borwein and Borwein?

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