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x+5

Sum of series x+5



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The solution

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  oo         
 __          
 \ `         
  )   (x + 5)
 /_,         
x = 0        
x=0(x+5)\sum_{x=0}^{\infty} \left(x + 5\right)
Sum(x + 5, (x, 0, oo))
The radius of convergence of the power series
Given number:
x+5x + 5
It is a series of species
ax(cxx0)dxa_{x} \left(c x - x_{0}\right)^{d x}
- power series.
The radius of convergence of a power series can be calculated by the formula:
Rd=x0+limxaxax+1cR^{d} = \frac{x_{0} + \lim_{x \to \infty} \left|{\frac{a_{x}}{a_{x + 1}}}\right|}{c}
In this case
ax=x+5a_{x} = x + 5
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=limx(x+5x+6)1 = \lim_{x \to \infty}\left(\frac{x + 5}{x + 6}\right)
Let's take the limit
we find
True

False
The rate of convergence of the power series
0.06.00.51.01.52.02.53.03.54.04.55.05.50100
The answer [src]
oo
\infty
oo
Numerical answer
The series diverges
The graph
Sum of series x+5

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