# Generating functions problem (stuck)

• Nov 29th 2010, 08:32 PM
guyonfire89
Generating functions problem (stuck)
From the integers:1,3 ,9,27,81,243,729...
I have:

The sum from k=0 to infin of 3^k times x^k.

How do I incorporate the geometric series into this and finish this problem?
• Nov 30th 2010, 12:04 AM
CaptainBlack
Quote:

Originally Posted by guyonfire89
From the integers:1,3 ,9,27,81,243,729...
I have:

The sum from k=0 to infin of 3^k times x^k.

How do I incorporate the geometric series into this and finish this problem?

$\displaystyle \sum_{k=0}^{\infty}3^kx^k=\sum_{k=0}^{\infty}(3x)^ k$

So if $3x<1$ you have a convergent infinite geometric series.

CB