Trail to infinity

Algebra Level 2

Let SS denote the infinite sum

112+122+132+142+. \dfrac{1}{1^2} + \dfrac{1}{2^2} + \dfrac{1}{3^2} + \dfrac{1}{4^2} + \cdots .

Find the value of

112+132+152+172+ \dfrac{1}{1^2} + \dfrac{1}{3^2} + \dfrac{1}{5^2} + \dfrac{1}{7^2} + \cdots

in terms of SS.

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