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n^2/2^n

  • How to use it?

  • Sum of series:
  • n^2/2^n n^2/2^n
  • 1/(n-1)! 1/(n-1)!
  • (3^n+4^n)/12^n (3^n+4^n)/12^n
  • 1/n^2 1/n^2

  • Identical expressions

  • n^ two / two ^n
  • n squared divide by 2 to the power of n
  • n to the power of two divide by two to the power of n
  • n2/2n
  • n²/2^n
  • n to the power of 2/2 to the power of n
  • n^2 divide by 2^n
Sum of series/ n^2/2^n

Sum of series n^2/2^n


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The solution

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

$$R = 0$$
The rate of convergence of the power series
The answer [src] 
6
$$6$$ 
6
Numerical answer [src] 
6.00000000000000000000000000000
6.00000000000000000000000000000
The graph
Sum of series n^2/2^n

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