Question

Find the exact sum of the following series

Answer 1

\[\sum_{n=0}^{\infty}\frac{ 3+3^n }{ 5^n }\]

Answer 2

I'd split it into two fractions so you have:

Sum to infinity of : (3/5^n) + (3/5)^n

You can then use the geometric series to obtain a sum to infinity of the entire sum.

The formula is for sum to infinity of x^n where x<1:
1/(1-x)

Answer 3

In this way you can evaluate:
3*(1/(1-(1/5)))=15/4

And

1/(1-(3/5)) = 5/2

So the answer should be 25/4 = 6.25

Answer 4

what other formula did you use ?

1/(1-x) and?

Answer 5

nevermind i got it