# Evaluate the sum

Calculus Level 5

Let $S=\sum_{n=1}^\infty (-1)^{n-1} \ln{\left(\frac{n+1}{n}\right)}$

Find the closed form for $$S$$, and enter your answer as $$\lfloor 10^6\times S \rfloor$$.

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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