Use the principle of mathematical induction to prove that is divisible by 6 for all n= ...
Lets start at the point assume and show that
We need to show that 6 divides
Now grouping the terms like this we get
The first group is divisible by 6 from the induction hypothsis 6 is obviously divisible by 6.
Notice that for every integer n is even and so it can be written in the form for some integer k.
this is also divisible by 6.