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sin(n)/n^(3/2)

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  • Sum of series:
  • sin(n)/n^(3/2) sin(n)/n^(3/2)
  • 1/n 1/n
  • 20 20
  • (n^11)^3:(n^5)^2 (n^11)^3:(n^5)^2

  • Identical expressions

  • sin(n)/n^(three / two)
  • sinus of (n) divide by n to the power of (3 divide by 2)
  • sinus of (n) divide by n to the power of (three divide by two)
  • sin(n)/n(3/2)
  • sinn/n3/2
  • sinn/n^3/2
  • sin(n) divide by n^(3 divide by 2)
Sum of series/ sin(n)/n^(3/2)

Sum of series sin(n)/n^(3/2)


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The solution

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

    Examples of finding the sum of a series

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