MATH307 December 2012
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If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
Parseval's formula says that
Calculate the integral on the left hand side and plug in the given and calculated values for cn on the right hand side. Then, isolate for
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Consider the Fourier series
for . Parseval’s formula says
Plugging in the left hand side we calculate
Plugging in the given and calculated values for cn in the right hand side we compute
Combining the left hand side and the right hand side of Parseval's formula we can find
Therefore, the infinite sum is
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