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(-1)n/2n-1

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



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The solution

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  oo             
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  \   /-n       \
   )  |---*n - 1|
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n = 1            
n=1(n(1)n21)\sum_{n=1}^{\infty} \left(n \frac{\left(-1\right) n}{2} - 1\right)
Sum(((-n)/2)*n - 1, (n, 1, oo))
The radius of convergence of the power series
Given number:
n(1)n21n \frac{\left(-1\right) n}{2} - 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=n221a_{n} = - \frac{n^{2}}{2} - 1
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=limn(n22+1(n+1)22+1)1 = \lim_{n \to \infty}\left(\frac{\frac{n^{2}}{2} + 1}{\frac{\left(n + 1\right)^{2}}{2} + 1}\right)
Let's take the limit
we find
True

False
The rate of convergence of the power series
1.07.01.52.02.53.03.54.04.55.05.56.06.5-100100
The answer [src]
-oo
-\infty
-oo
Numerical answer
The series diverges
The graph
Sum of series (-1)n/2n-1

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