Sum of series lnx

You have entered [src]

  oo        
 __         
 \ `        
  )   log(x)
 /_,        
x = 1

\sum_{x=1}^{\infty} \log{\left(x \right)}

Sum(log(x), (x, 1, oo))

The radius of convergence of the power series

Given number:

\log{\left(x \right)}

It is a series of species

a_{x} \left(c x - x_{0}\right)^{d x}

- power series.
The radius of convergence of a power series can be calculated by the formula:

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

In this case

a_{x} = \log{\left(x \right)}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{x \to \infty}\left(\frac{\left|{\log{\left(x \right)}}\right|}{\log{\left(x + 1 \right)}}\right)

True

False

The rate of convergence of the power series

Numerical answer

The series diverges

The graph