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1/(n(lnn)((ln)(lnn))^2)

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  • Sum of series:
  • lnn lnn
  • 1/(n(lnn)((ln)(lnn))^2) 1/(n(lnn)((ln)(lnn))^2)
  • (cos(nx)*3^n)/2^n
  • (n+1)/factorial(n) (n+1)/factorial(n)

  • Identical expressions

  • one /(n(lnn)((ln)(lnn))^ two)
  • 1 divide by (n(lnn)((ln)(lnn)) squared )
  • one divide by (n(lnn)((ln)(lnn)) to the power of two)
  • 1/(n(lnn)((ln)(lnn))2)
  • 1/nlnnlnlnn2
  • 1/(n(lnn)((ln)(lnn))²)
  • 1/(n(lnn)((ln)(lnn)) to the power of 2)
  • 1/nlnnlnlnn^2
  • 1 divide by (n(lnn)((ln)(lnn))^2)
Sum of series/ 1/(n(lnn)((ln)(lnn))^2)

Sum of series 1/(n(lnn)((ln)(lnn))^2)


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The solution

You have entered [src] 
  oo                           
____                           
\   `                          
 \                1            
  \   -------------------------
  /                           2
 /    n*log(n)*(log(n)*log(n)) 
/___,                          
n = 3
$$\sum_{n=3}^{\infty} \frac{1}{n \log{\left(n \right)} \left(\log{\left(n \right)} \log{\left(n \right)}\right)^{2}}$$ 
Sum(1/((n*log(n))*(log(n)*log(n))^2), (n, 3, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{n \log{\left(n \right)} \left(\log{\left(n \right)} \log{\left(n \right)}\right)^{2}}$$
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
$$a_{n} = \frac{1}{n \log{\left(n \right)}^{5}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right) \log{\left(n + 1 \right)}^{5} \left|{\frac{1}{\log{\left(n \right)}^{5}}}\right|}{n}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
  oo           
____           
\   `          
 \        1    
  \   ---------
  /        5   
 /    n*log (n)
/___,          
n = 3
$$\sum_{n=3}^{\infty} \frac{1}{n \log{\left(n \right)}^{5}}$$ 
Sum(1/(n*log(n)^5), (n, 3, oo))
The graph
Sum of series 1/(n(lnn)((ln)(lnn))^2)

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