Question

What is the sum of the infinite geometric series?

Answer 1

Answer: This series would have no last term. The general form of the infinite geometric series is a1+a1r+a1r2+a1r3+... , where a1 is the first term and r is the common ratio.

Step-by-step explanation:

Answer 2

Answer:

$S_{\infty}=\frac{80}{3}$

Step-by-step explanation:

The sum of an infinite geometric series is given by:

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

The given geometric series is

$\sum_{n=1}^{\infty}32(-\frac{1}{5})^{n-1}$

The constant ratio for this series is

$r=-\frac{1}{5}$

The first term of the series is $a=32(-\frac{1}{5})^{1-1}=32$

The sum to infinity is $S_{\infty}=\frac{32}{1--\frac{1}{5}}$

$\implies S_{\infty}=\frac{32}{\frac{6}{5}}=\frac{80}{3}$