# The sum of an infinite geometric series

1. Oct 20, 2008

### meeklobraca

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

1+(x+1)+(x+1)^2+(x+1)^3 + ..... if lx+1l < 1

2. Relevant equations

Sn=a/1-r

3. The attempt at a solution

My attempt:

so I have a = x+1 and r = x+1
from there i get x+1/1-(x+1)
which is x+1/1-x-1
from there x+1/-x
multiply by the reciprocal

my solution is x^2 + x + 1 with the 1 coming from the original sequence.

What do you think?

2. Oct 20, 2008

### dirk_mec1

I think the one should go and the answer is: -(x+1)/x (can you see why?)

3. Oct 20, 2008

### meeklobraca

So do I have everything correct until

from there x+1/-x?

If so then yes I see where you got it from.

x+1/-x the reciprocal is

x+1 multiplied by -1/x

correct?

4. Oct 20, 2008

### meeklobraca

Also, for this sequence, would 1 be the a variable? I have x+1 as the a variable but why wouldnt it be 1?

5. Oct 21, 2008

### HallsofIvy

Staff Emeritus
The first term in the series is 1. What does that tell you?

6. Oct 21, 2008

### meeklobraca

If 1 is the first term, then everything leading up to -(x+1)/x is wrong. So what is the first term?

If 1 is the first term then the answer is 1/-x? Can I leave the answer like that?

Last edited: Oct 21, 2008