Seems Like a Popular Problem!

Algebra Level 4

\[\left(1- \frac{1}{2^2}\right)\left(1- \frac{1}{3^2}\right)\left(1- \frac{1}{4^2}\right) \cdots \left(1- \frac{1}{2017^2}\right) \]

The expression above can expressed in a form of \( \frac{1}{n} + \frac{1}{m} \) where \(n \lt m\) are positive integers.

Find the value of \( 2017n + 2m \).


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