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n(n+1) (n+5) is a multiple of …

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n(n+1) (n+5) is a multiple of 3

Posted by Sanjay Bisht 7 years, 10 months ago

CBSE > Class 11 > Mathematics

1 answers

Harsh Dwivedi 7 years, 10 months ago

for P(1)= 1 2×6=12 which is multiple of 3 It is true then For P(K) = K(k+1) (k+5)=(k2+k) (k+5)=k3+5k2+k2+5k k3+6k2+5k =3m (where m is an integer) k3= 3m-6k2-5k Now for P(k+1)= K+1(k+2)(k+6) =on multiplying we get k3+9k2+20k+12 put k3= 3m-6k2-5k 3m-6k2-5k+9k2+20k+12 3(m-k2+5k+4) Hence P(k+1) is true And where n ~ natural no.

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