Sum of series with 1/2^n and 1/3^n terms

[Lance WIlliam]

Homework Statement

$$\Sigma$$ (1/2^n+1/3^n)
n=1

Homework Equations

The Attempt at a Solution

I get 7/2
by using a/1-r to both than adding...what am I doing wrong

2+3/2= 7/2

 

[Defennder]

I didn't get 7/2. Your technique seems ok. Must be some calculation error.

 

[Dick]

Homework Statement

$$\Sigma$$ (1/2^n+1/3^n)
n=1

Homework Equations

The Attempt at a Solution

I get 7/2
by using a/1-r to both than adding...what am I doing wrong

2+3/2= 7/2

You are using a/(1-r) with a=1. a is supposed to be the first term in the series. The sum starts at n=1.

 

[HallsofIvy]

The standard geometric series starts at n=0. These are not geometric series because they are missing the "n=0" term. Of course, for each of the two series, that would just be 1/2⁰= 1 and 1/3⁰= 1. Since those terms are missing, you need to subtract 2 from your result.