Using principle of mathematical induction prove that: \[ 1+\frac{1}...

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Using principle of mathematical induction prove that:
\[
1+\frac{1}{4}+\frac{1}{9}+\ldots+\frac{1}{n^{2}}2-\frac{1}{n} \text { for all } n \geq 2, n \in \mathbf{N} \text {. }
\]
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