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

Explanation

Let, `p(n) = 1/(3. 5)+1/(5. 7)+1/(7. 9)+...+1/((2n+1)(2n+3))=n/(3(2n+3))`.


For , n=1


L.H.S = `1/3.5 = 1/15`


R.H.S = `1 / (3(2(1)+3) = 1/15`


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