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sin(5/(n+1))

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  • Sum of series:
  • x^2j
  • 2i+1 2i+1
  • 3/n 3/n
  • 5000n+60000 5000n+60000

  • 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
∑n=1∞sin⁡(5n+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⁡(5n+1)\sin{\left(\frac{5}{n + 1} \right)}
It is a series of species
an(cx−x0)dna_{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:
Rd=x0+lim⁡n→∞∣anan+1∣cR^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}
In this case
an=sin⁡(5n+1)a_{n} = \sin{\left(\frac{5}{n + 1} \right)}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=lim⁡n→∞∣sin⁡(5n+1)sin⁡(5n+2)∣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
1.07.01.52.02.53.03.54.04.55.05.56.06.5010
Numerical answer [src] 
0.e+3
0.e+3
The graph
Sum of series sin(5/(n+1))

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