need homework help with geometric series

[corsec]

well I think this is a geometric series sorry for the lack of Sigma sign

find the sum of the series

6
Sigma 5(1/4)^n
n = 0

The problem i'm trying to get is how to start with the ratio

so using the finite geometric formula I should have

Sn = a(1 - r^n)
------------
r - 1

so

Sn = 5(1-(1/4)^n)
---------------
(1/4) - 1

Is this the correct approach or am I way off base here? so it has to be an exact answer I'm pretty sure I'm gonna have a huge fraction

 

[daon]

well I think this is a geometric series sorry for the lack of Sigma sign

find the sum of the series

6
Sigma 5(1/4)^n
n = 0

The problem i'm trying to get is how to start with the ratio

so using the finite geometric formula I should have

Sn = a(1 - r^n)
------------
r - 1

so

Sn = 5(1-(1/4)^n)
---------------
(1/4) - 1

Is this the correct approach or am I way off base here? so it has to be an exact answer I'm pretty sure I'm gonna have a huge fraction

Since |\(\displaystyle \frac{1}{4}\)| < 1, the sum is given by:

\(\displaystyle \frac{a}{1-r}\) = \(\displaystyle \frac{5}{1-\frac{1}{4}}\)