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(2*n-1)/2^n

  • How to use it?

  • Sum of series:
  • (2*n-1)/2^n (2*n-1)/2^n
  • arccot(x)
  • 1/((2n-1)(2n+1)) 1/((2n-1)(2n+1))
  • xi+xi

  • Identical expressions

  • (two *n- one)/ two ^n
  • (2 multiply by n minus 1) divide by 2 to the power of n
  • (two multiply by n minus one) divide by two to the power of n
  • (2*n-1)/2n
  • 2*n-1/2n
  • (2n-1)/2^n
  • (2n-1)/2n
  • 2n-1/2n
  • 2n-1/2^n
  • (2*n-1) divide by 2^n

  • Similar expressions

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

Sum of series (2*n-1)/2^n


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The solution

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

$$R = 0$$
The rate of convergence of the power series
The answer [src] 
3
$$3$$ 
3
Numerical answer [src] 
3.00000000000000000000000000000
3.00000000000000000000000000000
The graph
Sum of series (2*n-1)/2^n

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