 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ib/paper-2/3d/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

For

f = x^{2}

\int_{- 1}^{1} x^{4} d x = 2/5

a_{0} = 2/3

, and

a_{n} = 4 (- 1)^{n} / (π^{2} n^{2})

. Parseval yields

2/5 = 2/9 + 16 π^{- 4} \sum n^{- 4}

, hence

\sum n^{- 4} = π^{4} /90

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