Prove that `1/(n+1)+1/(n+2)+...+1/(2n)> 13/24` ,for all natural number `n>1`.

Explanation

Given,

`1/(n+1)+1/(n+2)+...+1/(2n)> 13/24`

`p(2)=1/2+1/4=3/4>13/24` which is true

`p(3)=1/2+1/4+1/6=11/12>13/24`

which is also true

Let p(k) be true,

now `p(k+1)=1/((k+1)+1)+1/((k+1)+2)+...+1/(2(k+1))`

`=1/(k+2)+1/(k+3)+....+1/((2k+2)`

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