# Sum of 3^r

• Nov 18th 2012, 10:24 AM
Mukilab
Sum of 3^r
How would I find the sum of 3^r from r=1 to r=n?

I honestly have no workings because I don't know how to approach this since I can't split it into 3*(sum[1^r])
Thank you for your help.
• Nov 18th 2012, 10:42 AM
Plato
Re: Sum of 3^r
Quote:

Originally Posted by Mukilab
How would I find the sum of 3^r from r=1 to r=n?

$\displaystyle \sum\limits_{k = 1}^n {t^k } = \frac{{t - t^{n + 1} }}{{1 - t}}$
• Nov 18th 2012, 04:53 PM
Prove It
Re: Sum of 3^r
Quote:

Originally Posted by Mukilab
How would I find the sum of 3^r from r=1 to r=n?

I honestly have no workings because I don't know how to approach this since I can't split it into 3*(sum[1^r])
Thank you for your help.

It's a geometric series with \displaystyle \displaystyle \begin{align*} a = 3 \end{align*} and common ratio \displaystyle \displaystyle \begin{align*} \rho = 3 \end{align*}.

The sum of a finite geometric series can be evaluated using \displaystyle \displaystyle \begin{align*} S_n = \frac{a \left( 1 - \rho ^n \right)}{1 - \rho} \end{align*}.