# 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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