# A series question

1. Aug 18, 2011

### GreenPrint

1. The problem statement, all variables and given/known data

Find the sum of the sereis 3 + 2 + 4/3 + 8/9 + 16/27 + ... and provide justification for your work.

2. Relevant equations

3. The attempt at a solution

I first thought that this was true

inf
sigma 2^k/3^(k-1)
k=0

This would be the correct series if we let the first term given in the series, given in the statement problem be the zeroth term and so on. I however had no idea how to find the sum of this series because of the different powers that occur in the numerator and denominator... thanks for any help

2. Aug 18, 2011

### ehild

Hint: write 3k-1 as (3k)(3-1).

ehild

3. Aug 18, 2011

### GreenPrint

*bangs head into desk* lol thanks

4. Aug 19, 2011

### Staff: Mentor

Not mentioned above is the fact that your series is a geometric series with ratio r = 2/3 and first term a = 3. Your text probably presented geometric series and arithmetic series before going on to other types of series.

5. Aug 19, 2011

### GreenPrint

Ya my text does and ya I figured this problem out and couldn't believe that I didn't see that