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Prove that n(n+1)(n+2)is divisible by 6?

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Prove that n(n+1)(n+2)is divisible by 6?

Posted by Arushi Sonal 3 years, 5 months ago

CBSE > Class 11 > Mathematics

1 answers

⠀ 3 years, 5 months ago

Let p(k) = n(n+1)(n+2) divisivle by 6
For n = 1 ,
p(k) is true
Let for n = k ,p(k) is true
For n = k+1:
(k+1)(k+2)(k+3)
k(k+1)(k+2)(k+3)/k divisible by 6
So by mathematical induction , statement is true for all n€N

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