Mister Exam

Other calculators

1/(n*ln^2n)

  • How to use it?

  • Sum of series:
  • 1/(n*ln^2n) 1/(n*ln^2n)
  • (3*n/(9*n-1))^n (3*n/(9*n-1))^n
  • log(1+1/n)/n log(1+1/n)/n
  • (5^n-2^n)/10^n (5^n-2^n)/10^n

  • Identical expressions

  • one /(n*ln^2n)
  • 1 divide by (n multiply by ln squared n)
  • one divide by (n multiply by ln squared n)
  • 1/(n*ln2n)
  • 1/n*ln2n
  • 1/(n*ln²n)
  • 1/(n*ln to the power of 2n)
  • 1/(nln^2n)
  • 1/(nln2n)
  • 1/nln2n
  • 1/nln^2n
  • 1 divide by (n*ln^2n)
Sum of series/ 1/(n*ln^2n)

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


∑
=

The solution

You have entered [src] 
  oo           
____           
\   `          
 \        1    
  \   ---------
  /        2   
 /    n*log (n)
/___,          
n = 1
∑n=1∞1nlog⁡(n)2\sum_{n=1}^{\infty} \frac{1}{n \log{\left(n \right)}^{2}} 
Sum(1/(n*log(n)^2), (n, 1, oo))
The radius of convergence of the power series
Given number:
1nlog⁡(n)2\frac{1}{n \log{\left(n \right)}^{2}}
It is a series of species
an(cx−x0)dna_{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:
Rd=x0+lim⁡n→∞∣anan+1∣cR^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}
In this case
an=1nlog⁡(n)2a_{n} = \frac{1}{n \log{\left(n \right)}^{2}}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=lim⁡n→∞((n+1)log⁡(n+1)2∣1log⁡(n)2∣n)1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right) \log{\left(n + 1 \right)}^{2} \left|{\frac{1}{\log{\left(n \right)}^{2}}}\right|}{n}\right)
Let's take the limit
we find
True

False
The rate of convergence of the power series
-0.010-0.008-0.006-0.004-0.0020.0100.0000.0020.0040.0060.0080.00
The graph
Sum of series 1/(n*ln^2n)

    Examples of finding the sum of a series

    © Mister Exam – Calculator