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(-1)^n/(2*n-1)

  • How to use it?

  • Sum of series:
  • 3i
  • n^2*x^n
  • (n^3+n+5)/(n+6) (n^3+n+5)/(n+6)
  • x^(n-1)/(n!)^(1/2)

  • Identical expressions

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

  • Similar expressions

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

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


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The solution

You have entered [src] 
  oo         
____         
\   `        
 \         n 
  \    (-1)  
  /   -------
 /    2*n - 1
/___,        
n = 1
$$\sum_{n=1}^{\infty} \frac{\left(-1\right)^{n}}{2 n - 1}$$ 
Sum((-1)^n/(2*n - 1), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\left(-1\right)^{n}}{2 n - 1}$$
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
$$a_{n} = \frac{1}{2 n - 1}$$
and
$$x_{0} = 1$$
,
$$d = 1$$
,
$$c = 0$$
then
$$R = \tilde{\infty} \left(1 + \lim_{n \to \infty}\left(\left(2 n + 1\right) \left|{\frac{1}{2 n - 1}}\right|\right)\right)$$
Let's take the limit
we find
False
The rate of convergence of the power series
The answer [src] 
-pi 
----
 4
$$- \frac{\pi}{4}$$ 
-pi/4
Numerical answer [src] 
-0.785398163397448309615660845820
-0.785398163397448309615660845820
The graph
Sum of series (-1)^n/(2*n-1)

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