Respuesta :

Ilyes39
It's geometric series:  [/tex] S_{n} [/tex]=[tex] \frac{1- 5^{n} }{1-5} [/tex]
[tex] S_{\infty} [/tex]=[tex] \frac{1}{-4} [/tex].

Answer:

[tex]\frac{125}{4}[/tex]

Step-by-step explanation:

evaluate the infinite series

25+5+1+ ...

Given series is geometric

Sum of geometric series formula is

[tex]S= \frac{a}{1-r}[/tex]

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

[tex]S=\frac{25}{1-\frac{1}{5}}[/tex]

[tex]S=\frac{25}{\frac{4}{5}}[/tex]

[tex]S=25*\frac{5}{4}[/tex]

[tex]S=\frac{125}{4}[/tex]

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