This is a example question on a practice exam, any help would be appreciated. It is attached. Using induction to prove it.
Thanks
For all integer ,
Sounds like your typical induction problem. Skipping the formalities ...
Inductive step
Assume it is true for , i.e. .
It remains to show that it is also true for , i.e.
But:
Factor out from the expression and you should get it equal to