Science:Math Exam Resources/Courses/MATH307/December 2010/Question 06 (c)/Statement

Explain how the orthogonality of the functions $e^{2\pi inx}$ allows you to relate the inner product in part (b) to the sum

$\sum _{n=-\infty }^{\infty }|c_{n}|^{2}$

Use your answer to to calculate the infinite sum

$\sum _{n=1}^{\infty }n^{-2}$