Obtain the Fourier series expansion of xsinx as a cosine series in (0, π)

Hi! Myself Dr. Ayan Sarkar. In this video regarding the half-range Fourier series, I have obtained the Fourier series representation of a function f(x) =xsinx, in the interval of 0 to π. Using the half-range Fourier cosine series expansion of xsinx (0, π), deduced herein, I have also found the value of the following series: 1+2/(1.3)-2/(3.5)+2/(5.7)- ... ... Please watch this video till the end and like this video, and subscribe to my channel. I have already uploaded several videos on Fourier series problems on my channel. To watch the videos, I would ask you to check the Fourier series and Physics classes playlists. I have collected the problem from the Higher Engineering Mathematics book, authored by Dr B.S. Grewal (38th edition); problem # 7, exercise 10.6. *Books I recommend for Fourier Series Analysis:* 1) Mathematical Methods for Physicists by Weber, Arfken Link: https://amzn.to/3wT7BFC 2) Higher Engineering Mathematics by B. S. Grewal Link: https://amzn.to/3Fr1pYn 3) Mathematical Physics by P. K. Chattopadhyay Link: https://amzn.to/3oynQ7f Prepare for NET/GATE (physics) Book Link: https://amzn.to/3npIVSd Book Link: https://amzn.to/3Cm4uqL GATE Physics Solved Papers: https://amzn.to/3Ho3ypP Hey! I have made this video using the Samsung Galaxy S6 tab. It's highly recommended to use. If you are a grad student you can have this pocket-friendly one. You can use a cool keyboard alongside, which will facilitate ease of working. Link of this Samsung Galaxy S6 tab in amazon.in: https://amzn.to/3Fr00B5 Keyboard for Galaxy S6: https://amzn.to/3Hxmx0Y Pocket-friendly iPad: https://amzn.to/3Ficawa