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sin(5/(n+1))

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  • Sum of series:
  • x^n/n
  • 1/(4n^2-1) 1/(4n^2-1)
  • (1000^n)/n! (1000^n)/n!
  • 2n 2n

  • Identical expressions

  • sin(five /(n+ one))
  • sinus of (5 divide by (n plus 1))
  • sinus of (five divide by (n plus one))
  • sin5/n+1
  • sin(5 divide by (n+1))

  • Similar expressions

  • sin(5/(n-1))
Sum of series/ sin(5/(n+1))

Sum of series sin(5/(n+1))


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The solution

You have entered [src] 
  oo            
 ___            
 \  `           
  \      /  5  \
   )  sin|-----|
  /      \n + 1/
 /__,           
n = 1
$$\sum_{n=1}^{\infty} \sin{\left(\frac{5}{n + 1} \right)}$$ 
Sum(sin(5/(n + 1)), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\sin{\left(\frac{5}{n + 1} \right)}$$
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
$$a_{n} = \sin{\left(\frac{5}{n + 1} \right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} \left|{\frac{\sin{\left(\frac{5}{n + 1} \right)}}{\sin{\left(\frac{5}{n + 2} \right)}}}\right|$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
Numerical answer [src] 
0.e+3
0.e+3
The graph
Sum of series sin(5/(n+1))

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