# Science:Math Exam Resources/Courses/MATH307/December 2012/Question 04 (d)

MATH307 December 2012

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### Question 04 (d)

Consider the Fourier series

${\displaystyle t^{2}-t=\sum _{n=-\infty }^{\infty }c_{n}e^{2\pi int}}$

for ${\displaystyle 0\leq t\leq 1}$.

(d) Given that ${\displaystyle c_{n}={\frac {1}{2\pi ^{2}n^{2}}}}$ for ${\displaystyle n\not =0}$, use Parseval's formula to find the value of the infinite sum ${\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{4}}}}$. Calculate a numerical expression - you do not need to simplify your answer.

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