Mister Exam

Other calculators

  • How to use it?

  • Sum of series:
  • sin(3n)/(7n)^(1/5) sin(3n)/(7n)^(1/5)
  • arctg1/(2n^2) arctg1/(2n^2)
  • cos(i*n)/2^n cos(i*n)/2^n
  • 1/(n*ln(n)*(ln(ln(n)))^2) 1/(n*ln(n)*(ln(ln(n)))^2)

  • Identical expressions

  • (twelve *ln(x))/(x^ three)
  • (12 multiply by ln(x)) divide by (x cubed )
  • (twelve multiply by ln(x)) divide by (x to the power of three)
  • (12*ln(x))/(x3)
  • 12*lnx/x3
  • (12*ln(x))/(x³)
  • (12*ln(x))/(x to the power of 3)
  • (12ln(x))/(x^3)
  • (12ln(x))/(x3)
  • 12lnx/x3
  • 12lnx/x^3
  • (12*ln(x)) divide by (x^3)
Sum of series/ (12*ln(x))/(x^3)

Sum of series (12*ln(x))/(x^3)


∑
=

The solution

You have entered [src] 
  oo           
____           
\   `          
 \    12*log(x)
  \   ---------
  /        3   
 /        x    
/___,          
n = 1
$$\sum_{n=1}^{\infty} \frac{12 \log{\left(x \right)}}{x^{3}}$$ 
Sum((12*log(x))/x^3, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{12 \log{\left(x \right)}}{x^{3}}$$
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
$$a_{n} = \frac{12 \log{\left(x \right)}}{x^{3}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
True

False
The answer [src] 
oo*log(x)
---------
     3   
    x
$$\frac{\infty \log{\left(x \right)}}{x^{3}}$$ 
oo*log(x)/x^3

    Examples of finding the sum of a series

    © Mister Exam – Calculator