Mathematics Tripos Papers

  • Part IA
  • Part IB
  • Part II
  • FAQ

4.I.5A

Methods | Part IB, 2008

Find the half-range Fourier cosine series for f(x)=x2,0<x<1f(x)=x^{2}, 0<x<1f(x)=x2,0<x<1. Hence show that

∑n=1∞1n2=π26.\sum_{n=1}^{\infty} \frac{1}{n^{2}}=\frac{\pi^{2}}{6} .n=1∑∞​n21​=6π2​.

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