Prove the following by the principle of mathematical induction: `1/(3. 5)+1/(5. 7)+1/(7. 9)+1/((2n+1)(2n+3))=n/(3(2n+3))`

Explanation

`P(n):1/(3⋅5)+1/(5⋅7)+1/(7⋅9)+…+1/((2n+1)(2n+3))=n/(3(2n+3)) `


Putting `n = 1` in the given statement, we get


`LHS =1/(3⋅5)=1/(15)` and


`RHS=1/(3(2×1+3))=1/(15) `


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