I believe IMO that summing binomial coefficients is very tricky. there are methods of induction to prove the result, but i think finding a way to come to actual result instead of M.induction is even better.

how to yield this result?? any help would be appreciated. Umm... btw i know the way of induction and yea i have proved it that way, but i want some ways in actually retrieving the result(say if the answer wasn't given).

thank you