The sum of an infinite geometric series

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Homework Help Overview

The discussion revolves around the evaluation of an infinite geometric series defined by the expression 1 + (x+1) + (x+1)^2 + (x+1)^3 + ... under the condition that |x+1| < 1. Participants are exploring the correct application of the formula for the sum of an infinite geometric series.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to identify the first term and common ratio of the series, with some suggesting that the first term is 1 while others argue for (x+1). There is also discussion about the implications of this choice on the final expression for the sum.

Discussion Status

The conversation is active, with participants questioning the correctness of previous steps and the identification of the first term. Some guidance has been offered regarding the implications of defining the first term as 1, leading to further exploration of the resulting expressions.

Contextual Notes

There is an ongoing debate about the definition of the first term in the series and its impact on the calculations, indicating potential misunderstandings about the series setup. Participants are also navigating the constraints imposed by the condition |x+1| < 1.

meeklobraca
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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?
 
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I think the one should go and the answer is: -(x+1)/x (can you see why?)
 
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?
 
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?
 
The first term in the series is 1. What does that tell you?
 
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:

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