Question

What is the sum of an infinite geometric series if 2=5 and r=1/3

Answer 1

Answer:

$\frac{15}{2}$

Step-by-step explanation:

The problem has a mistake, it should NOT be 2 = 5, rather a=5.

Now, given a = 5 (the first term is a), and

r = 1/3 (common ratio),

we can solve for the sum of the infinite series by using the formula:

$S_{\infty}=\frac{a}{1-r}$

Where $S_{\infty}$ is the sum of the infinite geometric series,

a is the first term (given as 5), and

r is the common ratio ( r= 1/3 given)

We now plug these into the formula and get our answer:

$S_{\infty}=\frac{a}{1-r}\\=\frac{5}{1-\frac{1}{3}}\\=\frac{5}{\frac{2}{3}}\\=\frac{15}{2}$