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  • Sum of series:
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  • Identical expressions

  • sinx*x^(five -x)
  • sinus of x multiply by x to the power of (5 minus x)
  • sinus of x multiply by x to the power of (five minus x)
  • sinx*x(5-x)
  • sinx*x5-x
  • sinxx^(5-x)
  • sinxx(5-x)
  • sinxx5-x
  • sinxx^5-x

  • Similar expressions

  • sinx*x^(5+x)
Sum of series/ sinx*x^(5-x)

Sum of series sinx*x^(5-x)


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The solution

You have entered [src] 
  oo                
 ___                
 \  `               
  \            5 - x
  /    sin(x)*x     
 /__,               
n = 10
$$\sum_{n=10}^{\infty} x^{5 - x} \sin{\left(x \right)}$$ 
Sum(sin(x)*x^(5 - x), (n, 10, oo))
The radius of convergence of the power series
Given number:
$$x^{5 - x} \sin{\left(x \right)}$$
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
$$a_{n} = x^{5 - x} \sin{\left(x \right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
True

False
The answer [src] 
    5 - x       
oo*x     *sin(x)
$$\infty x^{5 - x} \sin{\left(x \right)}$$ 
oo*x^(5 - x)*sin(x)

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