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n(n+1)(n+5) is a multiple of 3,,,, prove the following by using the principal of mathematical induction for all n€ N |
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Answer» -STEP explanation:For N=1, 1(1+1)(1+5)=12 which is a multiple of 3.Let it be TRUE for n=mso m(m+1)(m+5) = m³+6m²+5m is a multiple of 3.Say m³+6m²+5m= 3ASo for n =m+1,(m+1)(m+1+1)(m+1+5) = (m+1)(m+2)(m+6) = m³+9m²+20m+12 = m³+6m²+5m+ 3m²+15m+12 = 3A + 3(m² + 5m + 4) = 3[A + m²+5m + 4]Hence this is divisble by 3 |
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