Partial Fractions With A Side Of Pi

Algebra Level 3

Given that

113+1517+=π4,1-\dfrac{1}{3}+\dfrac{1}{5}-\dfrac{1}{7}+ \cdots = \dfrac{\pi}{4},

find the value of nn that satisfy the equation below:

11×3+15×7+19×11+=πn.\dfrac{1}{1 \times 3}+\dfrac{1}{5 \times 7}+\dfrac{1}{9 \times 11}+ \cdots = \dfrac{\pi}{n}.

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