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3^n/n^2

  • How to use it?

  • Sum of series:
  • (2/5)^n (2/5)^n
  • (2n+1)/(n^2(n+1)^2) (2n+1)/(n^2(n+1)^2)
  • 3^n/n^2 3^n/n^2
  • (5^n+4^n)/6^n (5^n+4^n)/6^n
  • Limit of the function:
  • 3^n/n^2 3^n/n^2

  • Identical expressions

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

Sum of series 3^n/n^2


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The solution

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

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