Finding the Sum of a Series with Justification | 3 + 2 + 4/3 + 8/9 + 16/27 + ...

[GreenPrint]

Homework Statement

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

Homework Equations

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

 

[ehild]

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

ehild

 

[GreenPrint]

*bangs head into desk* lol thanks

 

[Mark44]

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.

 

[GreenPrint]

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