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  • Sum of series:
  • sin(x)/n
  • sen(na)
  • log(1+3/n) log(1+3/n)
  • ln(1+3/n) ln(1+3/n)

  • Identical expressions

  • sinx/n^ three
  • sinus of x divide by n cubed
  • sinus of x divide by n to the power of three
  • sinx/n3
  • sinx/n³
  • sinx/n to the power of 3
  • sinx divide by n^3
Sum of series/ sinx/n^3

Sum of series sinx/n^3


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The solution

You have entered [src] 
  oo        
____        
\   `       
 \    sin(x)
  \   ------
  /      3  
 /      n   
/___,       
n = 1
$$\sum_{n=1}^{\infty} \frac{\sin{\left(x \right)}}{n^{3}}$$ 
Sum(sin(x)/n^3, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\sin{\left(x \right)}}{n^{3}}$$
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
$$a_{n} = \frac{\sin{\left(x \right)}}{n^{3}}$$
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] 
sin(x)*zeta(3)
$$\sin{\left(x \right)} \zeta\left(3\right)$$ 
sin(x)*zeta(3)

    Examples of finding the sum of a series

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