Prove that n2 + n is even , where n is natural number.?
step 1. put n=1
n2 + n = 12 +1 =2 which is even
step 2 . let assume result is true for n=k
then k2 +k is even number
step 3. to prove for n=k+1
(k+1)2 + (k+1)
= k2 + 1 + 2k + k + 1
= k2 + k + (2k +2)
i.e = even number + 2 (k+1) [using 1 . & 2(k+1) is also even ]
(also an even for all n belomgs to N)
therefore result is true for for all n belongs to N
hope it helps u