Prove by PMI :-n(n+1)(n+2)(n+3) is multiple of 24

1.	Prove by PMI :-n(n+1)(n+2)(n+3) is multiple of 24
Answer» For n=11(1+1)(1+2)(1+3)=1(2)(3)(4)=24For P(1) it is true.Let us assumes that it is true for n=kNow,P(k)=k(k+1)(k+2)(k+3)=24x(k+1)(k+2)(k+3)=24x/k.....(1)Now for P(k+1)=(k+1)(k+2)(k+3)(k+4)=24[x(k+4)/k]Therefore, it is true for n=k+1Thus by PMI, it is true for all n belongs to N

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