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sin((2*n+1)/n^3)

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  • Sum of series:
  • x^n/sqrt(n+1)
  • (1000^n)/n! (1000^n)/n!
  • 2n 2n
  • (x+3)^n/2^n

  • Identical expressions

  • sin((two *n+ one)/n^ three)
  • sinus of ((2 multiply by n plus 1) divide by n cubed )
  • sinus of ((two multiply by n plus one) divide by n to the power of three)
  • sin((2*n+1)/n3)
  • sin2*n+1/n3
  • sin((2*n+1)/n³)
  • sin((2*n+1)/n to the power of 3)
  • sin((2n+1)/n^3)
  • sin((2n+1)/n3)
  • sin2n+1/n3
  • sin2n+1/n^3
  • sin((2*n+1) divide by n^3)

  • Similar expressions

  • sin((2*n-1)/n^3)
Sum of series/ sin((2*n+1)/n^3)

Sum of series sin((2*n+1)/n^3)


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The solution

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

False
The rate of convergence of the power series
The graph
Sum of series sin((2*n+1)/n^3)

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