I have one question about a geometric series...please help. :)

**Caylie** · March 21st 2012, 06:16 AM

What are the first five partial sums of the geometric series (5/8)*3^(n-1)?

Any help is appreciated!

~Caylie

**princeps** · March 21st 2012, 06:43 AM

Originally Posted by Caylie

What are the first five partial sums of the geometric series (5/8)*3^(n-1)?

Any help is appreciated!

~Caylie

$\displaystyle \sum_{n=1}^5 \left(\frac{5}{8} \cdot 3^{n-1}\right)=\frac{5}{8} \cdot \displaystyle \sum_{n=1}^5 3^{n-1}=\frac{5}{8} \cdot \left(3^0+3^1+3^2+3^3+3^4\right)=\frac{605}{8}$

**emakarov** · March 21st 2012, 06:52 AM

Originally Posted by princeps

$\displaystyle \sum_{n=1}^5 \left(\frac{5}{8} \cdot 3^{n-1}\right)=\frac{5}{8} \cdot \displaystyle \sum_{n=1}^5 3^{n-1}=\frac{5}{8} \cdot \left(3^0+3^1+3^2+3^3+3^4\right)=\frac{605}{8}$

This is the fifth partial sum. The first four are formed similarly.

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