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logn/n^(5/4)

  • How to use it?

  • Sum of series:
  • 38 38
  • arctan(n)/(n!)^2 arctan(n)/(n!)^2
  • arctg(5/n)/n! arctg(5/n)/n!
  • ln((n^2+n+3)/(n^2+n+2)) ln((n^2+n+3)/(n^2+n+2))

  • Identical expressions

  • logn/n^(five / four)
  • logarithm of n divide by n to the power of (5 divide by 4)
  • logarithm of n divide by n to the power of (five divide by four)
  • logn/n(5/4)
  • logn/n5/4
  • logn/n^5/4
  • logn divide by n^(5 divide by 4)
Sum of series/ logn/n^(5/4)

Sum of series logn/n^(5/4)


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The solution

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

False
The rate of convergence of the power series
The graph
Sum of series logn/n^(5/4)

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