The value of the following conditionally convergent series can be expressed in the form \( \ln{(a)} + b \) where \( a \) and \( b \) are integers and the natural logarithm is fully simplified. What is the value of \( a + b \)?

\( \displaystyle \sum_{n=1}^{\infty} (-1)^{n} \frac{1}{n+1} \)

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