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(n+1)^2/2^(n-1)

  • How to use it?

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

  • Identical expressions

  • (n+ one)^ two / two ^(n- one)
  • (n plus 1) squared divide by 2 to the power of (n minus 1)
  • (n plus one) to the power of two divide by two to the power of (n minus one)
  • (n+1)2/2(n-1)
  • n+12/2n-1
  • (n+1)²/2^(n-1)
  • (n+1) to the power of 2/2 to the power of (n-1)
  • n+1^2/2^n-1
  • (n+1)^2 divide by 2^(n-1)

  • Similar expressions

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

Sum of series (n+1)^2/2^(n-1)


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The solution

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

False
The rate of convergence of the power series
The answer [src] 
22
$$22$$ 
22
Numerical answer [src] 
22.0000000000000000000000000000
22.0000000000000000000000000000
The graph
Sum of series (n+1)^2/2^(n-1)

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