Using the principle of mathematical induction prove that for all \(...

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Using the principle of mathematical induction prove that for all \( n \in N \) :
\[
\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\cdots \text { to } n \text { terms }=\frac{n}{2 n+1} .
\]
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