Mister Exam

Other calculators

((ln^2)n)/n

  • How to use it?

  • Sum of series:
  • (-1)^n/3^n (-1)^n/3^n
  • 3.8 3.8
  • 2^n/factorial(3*n) 2^n/factorial(3*n)
  • (sin*(pi/2^n))^n

  • Identical expressions

  • ((ln^ two)n)/n
  • ((ln squared )n) divide by n
  • ((ln to the power of two)n) divide by n
  • ((ln2)n)/n
  • ln2n/n
  • ((ln²)n)/n
  • ((ln to the power of 2)n)/n
  • ln^2n/n
  • ((ln^2)n) divide by n
Sum of series/ ((ln^2)n)/n

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


∑
=

The solution

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

False
The rate of convergence of the power series
The answer [src] 
  oo         
 ___         
 \  `        
  \      2   
  /   log (n)
 /__,        
n = 1
$$\sum_{n=1}^{\infty} \log{\left(n \right)}^{2}$$ 
Sum(log(n)^2, (n, 1, oo))
Numerical answer
The series diverges
The graph
Sum of series ((ln^2)n)/n

    Examples of finding the sum of a series

    © Mister Exam – Calculator