Infinite sums and products 3 (11)

Calculus Level 5

11232+13252+15272+ \large \dfrac1{1^2 \cdot 3^2} + \dfrac1{3^2 \cdot 5^2} + \dfrac1{5^2 \cdot 7^2} + \cdots

If the value of the series above is equal to πA+BC \dfrac{\pi^A + B}{C} , where A,BA,B and CC are integers, find the value of A+B+CA+B+C.

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