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1/(2n-1)

Sum of series 1/(2n-1)



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The solution

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  oo         
 ___         
 \  `        
  \      1   
   )  -------
  /   2*n - 1
 /__,        
n = 1        
n=112n1\sum_{n=1}^{\infty} \frac{1}{2 n - 1}
Sum(1/(2*n - 1), (n, 1, oo))
The radius of convergence of the power series
Given number:
12n1\frac{1}{2 n - 1}
It is a series of species
an(cxx0)dna_{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:
Rd=x0+limnanan+1cR^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}
In this case
an=12n1a_{n} = \frac{1}{2 n - 1}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=limn((2n+1)12n1)1 = \lim_{n \to \infty}\left(\left(2 n + 1\right) \left|{\frac{1}{2 n - 1}}\right|\right)
Let's take the limit
we find
True

False
The rate of convergence of the power series
1.07.01.52.02.53.03.54.04.55.05.56.06.502
The answer [src]
oo
\infty
oo
Numerical answer
The series diverges
The graph
Sum of series 1/(2n-1)

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