Prove the following by the principle of mathematical induction: `(1-1/(2^2))(1-1/(3^2))(1-1/(4^2))(1-1/(n^2))=(n+1)/(2n)` or all natural numbers`\ ngeq2.`

Explanation

`
(1-\frac{1}{2^{2}})(1-\frac{1}{3^{2}}) \ldots .(1-\frac{1}{n^{2}})=\frac{n+1}{2 n}
`
`\begin{array}{ll}\text { Given } n \geq 2 \\ \text { For } n=2\end{array} ` ` LHS =(1-\frac{1}{2^{2}})=1-\frac{1}{4}=\frac{3}{4}`
`RHS P (2)=\frac{2+1}{2(2)}=\frac{3}{4}`
`LHS = RHS`
`P (n)` is true for `n=2`
Assume that `P (n)` is true for `n=k`
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