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n^2/3^n

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  • Sum of series:
  • n^2/3^n n^2/3^n
  • (2^n+(-1)^n)/5^n (2^n+(-1)^n)/5^n
  • 1/(4n^2-1) 1/(4n^2-1)
  • (n+1)/n (n+1)/n

  • Identical expressions

  • n^ two / three ^n
  • n squared divide by 3 to the power of n
  • n to the power of two divide by three to the power of n
  • n2/3n
  • n²/3^n
  • n to the power of 2/3 to the power of n
  • n^2 divide by 3^n
Sum of series/ n^2/3^n

Sum of series n^2/3^n


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The solution

You have entered [src] 
  oo    
____    
\   `   
 \     2
  \   n 
   )  --
  /    n
 /    3 
/___,   
n = 1
$$\sum_{n=1}^{\infty} \frac{n^{2}}{3^{n}}$$ 
Sum(n^2/3^n, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{n^{2}}{3^{n}}$$
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
$$x_{0} = -3$$
,
$$d = -1$$
,
$$c = 0$$
then
$$\frac{1}{R} = \tilde{\infty} \left(-3 + \lim_{n \to \infty}\left(\frac{n^{2}}{\left(n + 1\right)^{2}}\right)\right)$$
Let's take the limit
we find
False

$$R = 0$$
The rate of convergence of the power series
The answer [src] 
3/2
$$\frac{3}{2}$$ 
3/2
Numerical answer [src] 
1.50000000000000000000000000000
1.50000000000000000000000000000
The graph
Sum of series n^2/3^n

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