Question

What is the sum of the geometric series sigma 15,x=0, 2(1/3)x​

Answer 1

Answer:

$\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0$

Step-by-step explanation:

We want to evaluate:

$\sum_{x=0}^{15}2(\frac{1}{3})^x$

When x=0, we obtain the first term of the geometric series as

$a_0=2(\frac{1}{3})^0$

The common ratio of this geometric series is $r=\frac{1}{3}$

The sum of the first n-terms of a geometric series is

$S_n=\frac{a(1-r^n)}{1-r}$

From x=0 to x=15, we have 16 terms.

The sum of the first 16 terms of the geometric series is

$S_{16}=\frac{a(1-(\frac{1}{3})^{16})}{1-\frac{1}{3}}=2.99999993031$

$\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0$ to the nearest tenth.