Mister Exam

Other calculators

  • How to use it?

  • Sum of series:
  • ((-1)^n)*((x^n)/(2n*n!))
  • (3-sin*n)/n-lnn (3-sin*n)/n-lnn
  • (7^n+3^n)/21^n (7^n+3^n)/21^n
  • log(1+1/n)-log(1+1/(n+1)) log(1+1/n)-log(1+1/(n+1))

  • 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)


∑
=

The solution

You have entered [src] 
  oo               
____               
\   `              
 \    sin(x)*sin(x)
  \   -------------
  /        2       
 /        x  + 1   
/___,              
n = 1
∑n=1∞sin⁡(x)sin⁡(x)x2+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:
sin⁡(x)sin⁡(x)x2+1\frac{\sin{\left(x \right)} \sin{\left(x \right)}}{x^{2} + 1}
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=sin⁡2(x)x2+1a_{n} = \frac{\sin^{2}{\left(x \right)}}{x^{2} + 1}
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] 
      2   
oo*sin (x)
----------
       2  
  1 + x
∞sin⁡2(x)x2+1\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

    © Mister Exam – Calculator