The sum of an infinite geometric series

[meeklobraca]

Homework Statement

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

Homework Equations

Sn=a/1-r

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?

 

[dirk_mec1]

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

 

[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?

 

[meeklobraca]

Also, for this sequence, would 1 be the a variable? I have x+1 as the a variable but why wouldn't it be 1?

 

[HallsofIvy]

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

 

[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?