# Homework Help: What is the value of the summation of (2^n+1)/3^n?

1. Apr 11, 2010

### IntegrateMe

So the question asks: What is the value of the "summation of" 2n+1/3n from "n=1 to infinity."

I changed 2n+1/3n into 2*(2/3)n so i could use it as a geometric series.

So now i just use the rule "a/(1-r) = sum" where a = first term and r = ratio i get 2/(1-(2/3)) which = 6. The answer is 4, any suggestions?

2. Apr 11, 2010

### gabbagabbahey

3. Apr 11, 2010

### VeeEight

4. Apr 11, 2010

### IntegrateMe

Oh wait, so the first term is 4/3 so i get (4/3)/[1-(2/3)] = 4. Thank you guys!

5. Apr 11, 2010

### gabbagabbahey

The $a$ in the numerator takes care of that.

$$\sum_{n=n_0}^\infty r^n=\frac{r^{n_0}}{1-r}=\frac{a}{1-r}$$

(When $r<1$ and $n_0\geq0$ of course)