how do you find the sum of this:
$$\sum_{n=0}^{15}2\left(\begin{matrix}4 \ 3\end{matrix}\right)^{n}$$

Question

how do you find the sum of this:
$$\sum_{n=0}^{15}2\left(\begin{matrix}4 \ 3\end{matrix}\right)^{n}$$

kinggeorge · Answer

Find $$\binom{4}{3}$$In this case, 4. Then use the expansion for a finite geometric series to find what the sum of $4^n$ from 0 to 15 is. Finally multiply by 2.

anonymous · Answer

can you show me the steps?

kinggeorge · Answer

$$\binom{4}{3}=4$$
The sum of a finite geometric series of $x^n$ from $n=0$ to $n=k$ is $$x^{k+1}-1 \over x-1 $$Thus, your sum should be $$2 \cdot \left({4^{16}-1 \over 4-1} \right)=2\cdot\left({4^{16}-1 \over 3}\right)$$You could calculate the actual number this gave you if you wanted to.

anonymous · Answer

so my answer woul be 28263311530?

kinggeorge · Answer

I'm getting 2863311530. 

I think you put an extra 2 in there.