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Sum of series/ ln((1-x)/(1+x))

Sum of series ln((1-x)/(1+x))


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The solution

You have entered [src] 
  oo            
 ___            
 \  `           
  \      /1 - x\
   )  log|-----|
  /      \1 + x/
 /__,           
n = 1
∑n=1∞log⁡(1−xx+1)\sum_{n=1}^{\infty} \log{\left(\frac{1 - x}{x + 1} \right)} 
Sum(log((1 - x)/(1 + x)), (n, 1, oo))
The radius of convergence of the power series
Given number:
log⁡(1−xx+1)\log{\left(\frac{1 - x}{x + 1} \right)}
It is a series of species
an(cx−x0)dna_{n} \left(c x - x_{0}\right)^{d n}
- power series.
The radius of convergence of a power series can be calculated by the formula:
Rd=x0+lim⁡n→∞∣anan+1∣cR^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}
In this case
an=log⁡(1−xx+1)a_{n} = \log{\left(\frac{1 - x}{x + 1} \right)}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=lim⁡n→∞11 = \lim_{n \to \infty} 1
Let's take the limit
we find
True

False
The answer [src] 
      /1 - x\
oo*log|-----|
      \1 + x/
∞log⁡(1−xx+1)\infty \log{\left(\frac{1 - x}{x + 1} \right)} 
oo*log((1 - x)/(1 + x))

    Examples of finding the sum of a series

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