Mister Exam

Other calculators

3*n/log(3*n)

  • How to use it?

  • Sum of series:
  • sin(n) sin(n)
  • (1+1/n)^n (1+1/n)^n
  • 14/49n^2-14n-48 14/49n^2-14n-48
  • 3*n/log(3*n) 3*n/log(3*n)

  • Identical expressions

  • three *n/log(three *n)
  • 3 multiply by n divide by logarithm of (3 multiply by n)
  • three multiply by n divide by logarithm of (three multiply by n)
  • 3n/log(3n)
  • 3n/log3n
  • 3*n divide by log(3*n)
Sum of series/ 3*n/log(3*n)

Sum of series 3*n/log(3*n)


∑
=

The solution

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

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

    Examples of finding the sum of a series

    © Mister Exam – Calculator