1. ## Hard series problem

Problem in image. I don't know how to start. I can do part b ok. help appreciated thanks

2. ## Re: Hard series problem

Hey GeeRaCeR.

I don't know what you have covered, but there is a result known as the Euler-Mclaurin formula which links sums, integrals, and error bounds together. Take a look at the wiki in relation to the basel problem (and also note that the basel problem can be written in terms of an integral with a fourier series decomposition):

Euler?Maclaurin formula - Wikipedia, the free encyclopedia

3. ## Re: Hard series problem

Hi,
The attachment shows an elementary derivation of the inequality of part a). I leave the other parts to you.