I've been having trouble with the following proof:
Let n be an odd positive integer. Prove that
+ + + ... + =
My first attempt at a proof was to use induction but at the inductive step, I couldn't simplify it to work out. After consulting my professor, he said that while it possible to prove it by induction, he could think of numerous other ways without induction. I'm not too sure of what to do now.
Yes I can see why for odd n that would hold true. (I expanded each combination and saw that the terms were equal in reverse order).
Now I just have to see how I can use this to relate my proof to the Binomial Theorem (?).
EDIT: Oh wait. Hm...
The proof is basically complete since the terms of each series are exactly equal. Is this correct?