# Summing +summing+summing...

Calculus Level 5

For n > 0, what is the value of $$\displaystyle\sum_{r=0}^{n} \left(-1\right)^r \binom{n}{r} \dfrac{1+r\ln 10}{\left(1+\ln 10^{n}\right)^{r}}$$?

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