# Homework Help: Sum of sequences

1. Nov 19, 2012

### nicnicman

1. The problem statement, all variables and given/known data

Find the sum of the sequence:
2, -2/3, 2/9, -2/27, 2/81, . . .

2. Relevant equations

3. The attempt at a solution

I can see that the number is multiplied by -1/3, but I'm unsure of how to find the sum.

Any pointers?

2. Nov 19, 2012

### hedipaldi

use the formula for the sum of geometric sequence.

3. Nov 19, 2012

### Staff: Mentor

This is a geometric sequence. There's a formula for finding the sum of a geometric series.

4. Nov 19, 2012

### FeynmanIsCool

an+1-1/a-1

5. Nov 19, 2012

### FeynmanIsCool

Summed over n: $\sum$ak=an+1-1/a-1

6. Nov 19, 2012

### Staff: Mentor

Use parentheses!

What you wrote is an + 1 - (1/a) - 1

7. Nov 19, 2012

### FeynmanIsCool

haha good note, your right. I have bad habits when it comes to those things

8. Nov 19, 2012

### nicnicman

Thanks for the help!

I came up with 1 41/81 using the formula. This also equals the sum of the numbers in the sequence (in my original post).

So, I guess it's correct.

9. Nov 19, 2012

### nicnicman

Although, this is in infinite geometric set so should I be using this formula:

S∞ = a1/(1-r), where a1 = the first term in the sequence, and r is the ratio.

Last edited: Nov 19, 2012
10. Nov 19, 2012

### nicnicman

So the answer would be 1 1/2. Correct?

11. Nov 19, 2012

### Dick

Yes, it's 3/2.

12. Nov 19, 2012

### nicnicman

Thanks for the reassurance.