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  • Sum of series:
  • sin(pi/n) sin(pi/n)
  • x^2/n^3
  • n(x^n)
  • (1-p)^(n-1)

  • Identical expressions

  • x^ two /n^ three
  • x squared divide by n cubed
  • x to the power of two divide by n to the power of three
  • x2/n3
  • x²/n³
  • x to the power of 2/n to the power of 3
  • x^2 divide by n^3
Sum of series/ x^2/n^3

Sum of series x^2/n^3


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The solution

You have entered [src] 
  oo    
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\   `   
 \     2
  \   x 
   )  --
  /    3
 /    n 
/___,   
n = 1
$$\sum_{n=1}^{\infty} \frac{x^{2}}{n^{3}}$$ 
Sum(x^2/n^3, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{x^{2}}{n^{3}}$$
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
$$a_{n} = \frac{x^{2}}{n^{3}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right)^{3}}{n^{3}}\right)$$
Let's take the limit
we find
True

False
The answer [src] 
 2        
x *zeta(3)
$$x^{2} \zeta\left(3\right)$$ 
x^2*zeta(3)

    Examples of finding the sum of a series

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