Question

prove by the prinnciple of mathmatical induction (n+1)(n+2) is divisible by 6 .....

Answer 1

check for n=1 will be (1+1)(1+2)=2*3=6 is true
for n=2 ----- (2+1)(2+2)=3*4=12 is true
suppose that this is true for n=k what will be (k+1)(k+2)
and you need to prove it for k=k+1 that this is true too
- so what will be ((k+1)+1)(k+1+2)=(k+2)(k+3)
- for k=1 we get 3*4 =12 is true

- from this resulted that (n+1)(n+2) is divisible by 6 is always true