You Gold to Be Kidding Me

Let \(\phi \ (N) \) denote the number of positive integers less than \( N \) and prime to it. Then evaluate the value of:-

\(\phi \ (1) \ \frac{5}{5^2 + 1} \ - \phi \ (3) \ \frac{125}{125^2+1} \ + \phi \ (5) \ \frac{3125}{3125^2+1} + \ldots \)

Note:- You might want to use a calculator in the last step. Round your answer to \( 3 \) decimal places.

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