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Sum of series/ ln(x)/(x^(5/4))

Sum of series ln(x)/(x^(5/4))


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The solution

You have entered [src] 
  oo        
____        
\   `       
 \    log(x)
  \   ------
  /     5/4 
 /     x    
/___,       
n = 1
$$\sum_{n=1}^{\infty} \frac{\log{\left(x \right)}}{x^{\frac{5}{4}}}$$ 
Sum(log(x)/x^(5/4), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\log{\left(x \right)}}{x^{\frac{5}{4}}}$$
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
$$a_{n} = \frac{\log{\left(x \right)}}{x^{\frac{5}{4}}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
True

False
The answer [src] 
oo*log(x)
---------
    5/4  
   x
$$\frac{\infty \log{\left(x \right)}}{x^{\frac{5}{4}}}$$ 
oo*log(x)/x^(5/4)

    Examples of finding the sum of a series

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