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  • Sum of series:
  • (-1/2)^n (-1/2)^n
  • 1/((2n+1)(2n+5)) 1/((2n+1)(2n+5))
  • 1/(n+2)^4 1/(n+2)^4
  • 1/(2n+5)(2n+7) 1/(2n+5)(2n+7)

  • Identical expressions

  • (sinx*sinx)/(x^ two + one)
  • ( sinus of x multiply by sinus of x) divide by (x squared plus 1)
  • ( sinus of x multiply by sinus of x) divide by (x to the power of two plus one)
  • (sinx*sinx)/(x2+1)
  • sinx*sinx/x2+1
  • (sinx*sinx)/(x²+1)
  • (sinx*sinx)/(x to the power of 2+1)
  • (sinxsinx)/(x^2+1)
  • (sinxsinx)/(x2+1)
  • sinxsinx/x2+1
  • sinxsinx/x^2+1
  • (sinx*sinx) divide by (x^2+1)

  • Similar expressions

  • (sinx*sinx)/(x^2-1)
Sum of series/ (sinx*sinx)/(x^2+1)

Sum of series (sinx*sinx)/(x^2+1)


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The solution

You have entered [src] 
  oo               
____               
\   `              
 \    sin(x)*sin(x)
  \   -------------
  /        2       
 /        x  + 1   
/___,              
n = 1
$$\sum_{n=1}^{\infty} \frac{\sin{\left(x \right)} \sin{\left(x \right)}}{x^{2} + 1}$$ 
Sum((sin(x)*sin(x))/(x^2 + 1), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\sin{\left(x \right)} \sin{\left(x \right)}}{x^{2} + 1}$$
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
$$a_{n} = \frac{\sin^{2}{\left(x \right)}}{x^{2} + 1}$$
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] 
      2   
oo*sin (x)
----------
       2  
  1 + x
$$\frac{\infty \sin^{2}{\left(x \right)}}{x^{2} + 1}$$ 
oo*sin(x)^2/(1 + x^2)

    Examples of finding the sum of a series

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