Mister Exam

Other calculators

  • How to use it?

  • Sum of series:
  • 1/ln(n+1) 1/ln(n+1)
  • factorial(k) factorial(k)
  • chx/(shx^2+1)
  • (2/3)^n (2/3)^n

  • Identical expressions

  • chx/(shx^ two + one)
  • chx divide by (shx squared plus 1)
  • chx divide by (shx to the power of two plus one)
  • chx/(shx2+1)
  • chx/shx2+1
  • chx/(shx²+1)
  • chx/(shx to the power of 2+1)
  • chx/shx^2+1
  • chx divide by (shx^2+1)

  • Similar expressions

  • chx/(shx^2-1)
Sum of series/ chx/(shx^2+1)

Sum of series chx/(shx^2+1)


∑
=

The solution

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

    Examples of finding the sum of a series

    © Mister Exam – Calculator