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n(n+1)(n+5) is multiple of 3 |
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Answer» To verify : n(n+1)(n+5) is divisible by 3 or notLet us use Principle of InductionLet f(n) = n(n+1)(n+5) = n3+6n2+5nLet us verify for n= 1: f(1) = 12 = 3*4 ; Hence f(n) is divisible by 3 for n = 1Let us assume that f(n) is divisible by 3 for any natural number n = aThat is f(a) = a3+6a2+5a = 3 (m) ;Let us Prove that f(a+1) is also divisible by 3 if f(a) is divisible by 3f(a+1) = (a+1)3+6(a+1)2+5(a+1) = a3+9a2+20a+12 = (a3+6a2+5a)+3a2+15a+12 = 3m+3a2+15a+12= 3(m+a2+5a+4); Hence f(a+1) is also divisible by 3.Hence it is TRUE that n(n+1)(n+5) is divisible by 3 Hi you are manjeet and I am manjit |
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