1. ## Binomial Thm

Use the binomial theorem to Prove:

The sum as k=0 --> n OF (nCk)*2^k = 3^n

Thanks...

2. So you want to prove that

$\displaystyle\sum_{k=0}^{n}{n\choose k} 2^{k}=3^{n},$ right?

Have you had any ideas so far?

3. Yes thats correct. And no, I don't see what to do...

4. Originally Posted by jzellt
And no, I don't see what to do...
Hint: 1 to any power is 1, i.e. $1 = (1)^{n-k}$.

5. I just really don't see this one. Is it possible for someone to show me the proof? Thanks

6. $(a+b)^n=\displaytype{\sum_{k=0}^n \binom{n}{k}b^ka^{n-k}}$

consider a=1 and b=2

7. I think I can go from here... Thanks!