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

Explanation

Given,

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

p(k) is true. for n=1

let P(k)be true for n=k

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


let `p(k+1)` be also true.

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