Representing a Sum of a Series as a Function

[color_me]

Homework Statement

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Find a function to represent the series and then find f(?) that will represent its sum.

Homework Equations

The Attempt at a Solution

I kind of understand how to come up with a function, but then how do I know what value to plug into the function to get the sum? Thank you for any help!

 

[zcd]

it should help to know that \tan{x}=\sum_{n=0}^{\infty}(-1)^{n}\frac{x^{2n+1}}{2n+1}