Mister Exam

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Sum of series/ 1/lnx

Sum of series 1/lnx

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  oo        
 ___        
 \  `       
  \     1   
   )  ------
  /   log(x)
 /__,       
n = 1

\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:

\frac{1}{\log{\left(x \right)}}

It is a series of species

a_{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:

R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}

In this case

a_{n} = \frac{1}{\log{\left(x \right)}}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty} 1

True

False

The answer [src]

  oo  
------
log(x)

\frac{\infty}{\log{\left(x \right)}}

oo/log(x)