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Sum of series 1/lnx



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The solution

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  oo        
 ___        
 \  `       
  \     1   
   )  ------
  /   log(x)
 /__,       
n = 1       
n=11log(x)\sum_{n=1}^{\infty} \frac{1}{\log{\left(x \right)}}
Sum(1/log(x), (n, 1, oo))
The radius of convergence of the power series
Given number:
1log(x)\frac{1}{\log{\left(x \right)}}
It is a series of species
an(cxx0)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+limnanan+1cR^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}
In this case
an=1log(x)a_{n} = \frac{1}{\log{\left(x \right)}}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=limn11 = \lim_{n \to \infty} 1
Let's take the limit
we find
True

False
The answer [src]
  oo  
------
log(x)
log(x)\frac{\infty}{\log{\left(x \right)}}
oo/log(x)

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