Sum of combinatoric coefficients with sum of reciprocals??

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Consider a function \(f(n) \) defined as :

\(f(n) = \sum _{r=1}^n (-1)^{r+1} {n \choose r}\) ( \(\sum_{k=1}^r \frac{1}{k}\))

Find the value of:

\(\sum_{i=1}^\infty (-1)^{i+1} f(i) \)

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