Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2021 / Paper 2 / 18 / e / Solution

Here $f(x{)}^2=x^2$, soSubstituting the coefficients from part (b) into Parseval's identity givesHence the sum over all positive odd integers is ${\pi }^4/96$. The requested series starts at $n=1$, whose first denominator is $3^4$, so it excludes the contribution $1^{-4}$: