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sinn/(n^4)

  • How to use it?

  • Sum of series:
  • n*2^n n*2^n
  • 1/((3n+1)*(3n+4)) 1/((3n+1)*(3n+4))
  • 1/(2*n+5)*(2*n+7) 1/(2*n+5)*(2*n+7)
  • x(x-1) x(x-1)

  • Identical expressions

  • sinn/(n^ four)
  • sinus of n divide by (n to the power of 4)
  • sinus of n divide by (n to the power of four)
  • sinn/(n4)
  • sinn/n4
  • sinn/(n⁴)
  • sinn/n^4
  • sinn divide by (n^4)
Sum of series/ sinn/(n^4)

Sum of series sinn/(n^4)


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The solution

You have entered [src] 
  oo        
____        
\   `       
 \    sin(n)
  \   ------
  /      4  
 /      n   
/___,       
n = 1
$$\sum_{n=1}^{\infty} \frac{\sin{\left(n \right)}}{n^{4}}$$ 
Sum(sin(n)/n^4, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\sin{\left(n \right)}}{n^{4}}$$
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
$$a_{n} = \frac{\sin{\left(n \right)}}{n^{4}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right)^{4} \left|{\frac{\sin{\left(n \right)}}{\sin{\left(n + 1 \right)}}}\right|}{n^{4}}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
Numerical answer
The series diverges
The graph
Sum of series sinn/(n^4)

    Examples of finding the sum of a series

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