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2^n/n^2

  • How to use it?

  • Sum of series:
  • 2^n/n^2 2^n/n^2
  • (n-1)/2^(n+1) (n-1)/2^(n+1)
  • 2^(2*n-1)/9^n 2^(2*n-1)/9^n
  • 1/4^1 1/4^1

  • Identical expressions

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

Sum of series 2^n/n^2


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The solution

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

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