Sum of 3^r

**Mukilab** · November 18th 2012, 10:24 AM

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.

**Plato** · November 18th 2012, 10:42 AM

Originally Posted by Mukilab

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

$\sum\limits_{k = 1}^n {t^k } = \frac{{t - t^{n + 1} }}{{1 - t}}$

**Prove It** · November 18th 2012, 04:53 PM

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 $\displaystyle \begin{align*} a = 3 \end{align*}$ and common ratio $\displaystyle \begin{align*} \rho = 3 \end{align*}$ .

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

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