For which numbers is this convergence?

AI Thread Summary
The discussion focuses on determining the convergence of an infinite geometric series defined by a=x/(x+1). The series converges when the absolute value of a is less than one, specifically for |a|<1. Participants suggest using the d'Alembert ratio test to analyze convergence. The key task is to find the range of x values for which this condition holds true. Understanding these parameters is essential for establishing the convergence of the series.
venke
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Hi,

I need to know for which nubers of x the serie is convergence.

1.JPG


Is this possible whith d'Alombert? I have tried, but with no result.

Greets,
venke
 
Mathematics news on Phys.org
Your series is an infinite geometric series with a=x/(x+1). This series converges for |a|<1. You should be able to find what is the range of x for convergence.
 

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