Fun with Logarithms

Algebra Level 2

\[\log_{2}\left(1+\frac{1}{2}\right)+\log_{2}\left(1+\frac{1}{3}\right)+\log_{2}\left(1+\frac{1}{4}\right)+\cdots+\log_{2}\left(1+\frac{1}{31}\right)=\, ?\]

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