Question

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

Answer 1

It's geometric series: [/tex] S_{n} [/tex]=
`(1- 5^(n) )/(1-5)`

`S_(\infty)`=
`(1)/(-4)`.

Answer 2

`(125)/(4)`

Explanation:

evaluate the infinite series

25+5+1+ ...

Given series is geometric

Sum of geometric series formula is

`S= (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=(25)/(1-(1)/(5))`

`S=(25)/((4)/(5))`

`S=25*(5)/(4)`

`S=(125)/(4)`