Prove by the principle of mathematical induction that for all `n in N ,n^2+n` is even natural number.

Explanation

let `p(n)=n^2+n`

`p(1)=1^2+1=2` which is even

`p(2)=2^2+2 =6 `which is even.

so,p(k) is even.

now for `p(k+1)`

`=(k+1)^2+(k+1)`

`=k^2+2k+1+k+1`

`=k^2+k+2(k+1)`

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