Question

Use the formula to evaluate the infinite series. Round to the nearest hundredth if necessary. 25+5+1+ ...

Answer 1

Answer:

$\frac{125}{4}$

Step-by-step explanation:

evaluate the infinite series

25+5+1+ ...

Given series is geometric

Sum of geometric series formula is

$S= \frac{a}{1-r}$

Where 'a' is the first term

'r' is the common ratio

to get common ratio divide second term by first term

5/25= 1/5

so a= 25  and r= 1/5

$S=\frac{25}{1-\frac{1}{5}}$

$S=\frac{25}{\frac{4}{5}}$

$S=25*\frac{5}{4}$

$S=\frac{125}{4}$

Answer 2

It's geometric series:  [/tex] S_{n} [/tex]=$\frac{1- 5^{n} }{1-5}$
$S_{\infty}$=$\frac{1}{-4}$.