what are the partial sums of the sequence

Question

For the sequence An= (2)/(3ⁿ),

 

its fifth partial sum S₅=

its nth partial sum S_n=

 

Answer 1

2/3 + 2/9 = (6+2)/9 = 8/9

2/3 + 2/9+2/27 = (24+2)/27 = 26/27

2/3+2/9+2/27+2/81 = 80/81

 

1st partial sum       2/3

2nd partial sum     8/9

3rd partial sum       26/27

4th partial sum        80/81

 

Notice a pattern?

What is the pattern for the denominator?
How do you get the numerator after you have the denominator?