Mathematics: What is the sum of the infinite geometric series?

What is the sum of the infinite geometric series?

gldven7636

10.03.2022

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

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 $S_{\infty}=\frac{32}{1--\frac{1}{5}}$

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

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stephanieeping

01.03.2022

50cm

step-by-step explanation:

perimeter: 2*width+2*length

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