Urgent! Difficult Discrete methods (2)?

Question

Prove :
the summation (sigma) of (n choose k) *5^k where k is odd and starts from 1 to n = ( 6^n - (-4)^n ) / 2

Answer 1

nC0-nC1*5+nC2*5^2...=(1-5)^n
again nCo+nC1*5+nC2*5^2...=(1+5)^n
subtracting we get 6^n-(-4)^n=2(nc1*5+nC2*5^3..
so the answer is proved.
p.s. do not listen to john w. use induction here and get a zero. i doubt if he knows how to solve the problem at all

Answer 2

I like soumyo's solution. I didn't even bother writing it out before I answer this.

P.S. next time, show everyone what effort you have made before asking. It is rude to ask others to solve a homework problem in its entirety for you without telling them what you have done/tried.


=== to soumyo ===
i would have known it if i bothered to solve it for him at all. but either way your solution is good, just try to sound less provocative next time. There are better ways to point out others mistakes