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Sum of series/ sh(x)

Sum of series sh(x)


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The solution

You have entered [src] 
  oo         
 __          
 \ `         
  )   sinh(x)
 /_,         
n = 0
∑n=0∞sinh⁡(x)\sum_{n=0}^{\infty} \sinh{\left(x \right)} 
Sum(sinh(x), (n, 0, oo))
The radius of convergence of the power series
Given number:
sinh⁡(x)\sinh{\left(x \right)}
It is a series of species
an(cx−x0)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+lim⁡n→∞∣anan+1∣cR^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}
In this case
an=sinh⁡(x)a_{n} = \sinh{\left(x \right)}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=lim⁡n→∞11 = \lim_{n \to \infty} 1
Let's take the limit
we find
True

False
The answer [src] 
oo*sinh(x)
∞sinh⁡(x)\infty \sinh{\left(x \right)} 
oo*sinh(x)

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