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Sum of series sinx/(x^p+sinx)

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  oo             
____             
\   `            
 \       sin(x)  
  \   -----------
  /    p         
 /    x  + sin(x)
/___,            
n = 0

\sum_{n=0}^{\infty} \frac{\sin{\left(x \right)}}{x^{p} + \sin{\left(x \right)}}

Sum(sin(x)/(x^p + sin(x)), (n, 0, oo))

The radius of convergence of the power series

Given number:

\frac{\sin{\left(x \right)}}{x^{p} + \sin{\left(x \right)}}

It is a series of species

a_{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:

R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}

In this case

a_{n} = \frac{\sin{\left(x \right)}}{x^{p} + \sin{\left(x \right)}}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty} 1

True

False

The answer [src]

 oo*sin(x) 
-----------
 p         
x  + sin(x)

\frac{\infty \sin{\left(x \right)}}{x^{p} + \sin{\left(x \right)}}

oo*sin(x)/(x^p + sin(x))