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ln^n2/3^n

  • 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)
  • tan(n*x)
  • ln^n2/3^n ln^n2/3^n

  • Identical expressions

  • ln^n2/ three ^n
  • ln to the power of n2 divide by 3 to the power of n
  • ln to the power of n2 divide by three to the power of n
  • lnn2/3n
  • ln^n2 divide by 3^n
Sum of series/ ln^n2/3^n

Sum of series ln^n2/3^n


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The solution

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

False

$$R = 0$$
The rate of convergence of the power series
The answer [src] 
    log(2)    
--------------
  /    log(2)\
3*|1 - ------|
  \      3   /
$$\frac{\log{\left(2 \right)}}{3 \left(1 - \frac{\log{\left(2 \right)}}{3}\right)}$$ 
log(2)/(3*(1 - log(2)/3))
Numerical answer [src] 
0.300473083813033985975954615589
0.300473083813033985975954615589
The graph
Sum of series ln^n2/3^n

    Examples of finding the sum of a series

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