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sqrt(n)*sin(pi/2)

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  • Sum of series:
  • 9/(9n^2+21n-8) 9/(9n^2+21n-8)
  • 7^x/(5^x-3)
  • 38 38
  • sqrt(n)*sin(pi/2) sqrt(n)*sin(pi/2)

  • Identical expressions

  • sqrt(n)*sin(pi/ two)
  • square root of (n) multiply by sinus of ( Pi divide by 2)
  • square root of (n) multiply by sinus of ( Pi divide by two)
  • √(n)*sin(pi/2)
  • sqrt(n)sin(pi/2)
  • sqrtnsinpi/2
  • sqrt(n)*sin(pi divide by 2)
Sum of series/ sqrt(n)*sin(pi/2)

Sum of series sqrt(n)*sin(pi/2)


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The solution

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

False
The rate of convergence of the power series
The answer [src] 
  oo       
 ___       
 \  `      
  \     ___
  /   \/ n 
 /__,      
n = 1
$$\sum_{n=1}^{\infty} \sqrt{n}$$ 
Sum(sqrt(n), (n, 1, oo))
The graph
Sum of series sqrt(n)*sin(pi/2)

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