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Sum of series cos(x+y)



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The solution

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  oo            
 __             
 \ `            
  )   cos(x + y)
 /_,            
n = 1           
n=1cos(x+y)\sum_{n=1}^{\infty} \cos{\left(x + y \right)}
Sum(cos(x + y), (n, 1, oo))
The radius of convergence of the power series
Given number:
cos(x+y)\cos{\left(x + y \right)}
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=cos(x+y)a_{n} = \cos{\left(x + y \right)}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=limn11 = \lim_{n \to \infty} 1
Let's take the limit
we find
True

False
The answer [src]
oo*cos(x + y)
cos(x+y)\infty \cos{\left(x + y \right)}
oo*cos(x + y)

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