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  • Sum of series:
  • (n+1)^2/2^(n-1) (n+1)^2/2^(n-1)
  • (-1)^n/n (-1)^n/n
  • (5/6)^n (5/6)^n
  • 28 28

  • Identical expressions

  • one /((x(x+ one)))^(one / two)
  • 1 divide by ((x(x plus 1))) to the power of (1 divide by 2)
  • one divide by ((x(x plus one))) to the power of (one divide by two)
  • 1/((x(x+1)))(1/2)
  • 1/xx+11/2
  • 1/xx+1^1/2
  • 1 divide by ((x(x+1)))^(1 divide by 2)

  • Similar expressions

  • 1/((x(x-1)))^(1/2)
Sum of series/ 1/((x(x+1)))^(1/2)

Sum of series 1/((x(x+1)))^(1/2)


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The solution

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

False
The answer [src] 
      oo     
-------------
  ___________
\/ x*(1 + x)
$$\frac{\infty}{\sqrt{x \left(x + 1\right)}}$$ 
oo/sqrt(x*(1 + x))

    Examples of finding the sum of a series

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