Question

n(n+1)(n+5) is a multiple of 3,,,, prove the following by using the principal of mathematical induction for all n€ N​

Answer 1

Step-by-step explanation:

For n=1, 1(1+1)(1+5)=12 which is a multiple of 3.

Let it be true for n=m

so m(m+1)(m+5) = m³+6m²+5m is a multiple of 3.

Say m³+6m²+5m= 3A

So 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