Prove by mathematical induction that n(n+1) is even.

1.	Prove by mathematical induction that n(n+1) is even.
Answer» step 1 p(n) = 1 1 (1+1) = 1 x 2 = 2 p (1) is true step 2 let p(k) = k (k+1) = 2 z where z is a natural no. be true k2 + k =2 z k2 = 2 z - k - 1 step 3 p(k+1) = k+1(k +1 +1) is true we have to prove this (k+1)( k+2) = k2 + 3 k + 2 2 z - k +3 k +2 = 2 z + 2 k + 2 - by 1 2[ z +k + 1] it will be a even no. which means that p(k+1) is true

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