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Using the principle of mathematical induction prove that for all \( n \in N \) :
\[
\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right) \cdots\left(1-\frac{1}{n+1}\right)=\frac{1}{n+1} \text {. }
\]
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