Mister Exam

Other calculators

1/(n*sqrt(log(n)))

  • How to use it?

  • Sum of series:
  • 1/(n*sqrt(log(n))) 1/(n*sqrt(log(n)))
  • cos(n*x)
  • 2^k 2^k
  • (x+1)
  • Limit of the function:
  • 1/(n*sqrt(log(n))) 1/(n*sqrt(log(n)))

  • Identical expressions

  • one /(n*sqrt(log(n)))
  • 1 divide by (n multiply by square root of ( logarithm of (n)))
  • one divide by (n multiply by square root of ( logarithm of (n)))
  • 1/(n*√(log(n)))
  • 1/(nsqrt(log(n)))
  • 1/nsqrtlogn
  • 1 divide by (n*sqrt(log(n)))
Sum of series/ 1/(n*sqrt(log(n)))

Sum of series 1/(n*sqrt(log(n)))


∑
=

The solution

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

False
The rate of convergence of the power series
The graph
Sum of series 1/(n*sqrt(log(n)))

    Examples of finding the sum of a series

    © Mister Exam – Calculator