Prove that n2 + n is even , where n is natural number.?

step 1. put n=1

n+ 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

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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
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