Geometric series Help!

Question

angelwings996 · Answer

What is the sum of the geometric series $$\sum_{x=0}^{15}z2(1/2)^{x}$$ rounded to the nearest whole numer?

angelwings996 · Answer

@ParthKohli could you help me?

anonymous · Answer

$$\Large \sum_{x=0}^{15}2\cdot \left(\frac{1}{2}\right)^x $$
Like that? there shouldn't be an x in front of the $a$ term in case it's strictly geometric.

angelwings996 · Answer

It shows a z infront of the 2, i don't know why

anonymous · Answer

hmm in this case it would need specification what the $z$ is about, if it is an integer number, for the problem it makes not much sense. Maybe you have an answer and we can check with that later on. If not, maybe someone else has an idea how to treat that variable.

Anyhow, here's the formula for the geometric series (runtime zero to n)

$$\Large s_n=a_1\left(\frac{1-q^{n+1}}{1-q} \right) $$

Where $a_1$ is the initial term, in your case $2$ or maybe (which makes no sense in my opinion) $2z$ and $q$ is the ratio given the problem, in your case 1/2

angelwings996 · Answer

This is a muliple choice problem:

A. 4
B. 0
C. 2
D. 3

angelwings996 · Answer

But it doesn't tell what z is so that is why I am confused on this problem because I don't know what to do for the z

anonymous · Answer

oh, I see, in this case z is a printing error.

angelwings996 · Answer

Should I just solve and leave out the z and see if I get one of the answers that are given?

anonymous · Answer

exactly