Mister Exam

Other calculators

(-cos(n*(pi))/(n*(pi)))*(sen((n*(pi)))/2)

  • How to use it?

  • Sum of series:
  • 1/((3n-2)(3n+1)) 1/((3n-2)(3n+1))
  • 3/(n(n+2)) 3/(n(n+2))
  • 6/9n^2+12n-5 6/9n^2+12n-5
  • 3i

  • Identical expressions

  • (-cos(n*(pi))/(n*(pi)))*(sen((n*(pi)))/ two)
  • ( minus co sinus of e of (n multiply by ( Pi )) divide by (n multiply by ( Pi ))) multiply by (sen((n multiply by ( Pi ))) divide by 2)
  • ( minus co sinus of e of (n multiply by ( Pi )) divide by (n multiply by ( Pi ))) multiply by (sen((n multiply by ( Pi ))) divide by two)
  • (-cos(n(pi))/(n(pi)))(sen((n(pi)))/2)
  • -cosnpi/npisennpi/2
  • (-cos(n*(pi)) divide by (n*(pi)))*(sen((n*(pi))) divide by 2)

  • Similar expressions

  • (cos(n*(pi))/(n*(pi)))*(sen((n*(pi)))/2)
Sum of series/ (-cos(n*(pi))/(n*(pi)))*(sen((n*(pi)))/2)

Sum of series (-cos(n*(pi))/(n*(pi)))*(sen((n*(pi)))/2)


∑
=

The solution

You have entered [src] 
  oo                       
 ___                       
 \  `                      
  \   -cos(n*pi)  sin(n*pi)
   )  -----------*---------
  /       n*pi        2    
 /__,                      
n = 1
$$\sum_{n=1}^{\infty} \frac{\sin{\left(\pi n \right)}}{2} \frac{\left(-1\right) \cos{\left(\pi n \right)}}{\pi n}$$ 
Sum(((-cos(n*pi))/((n*pi)))*(sin(n*pi)/2), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\sin{\left(\pi n \right)}}{2} \frac{\left(-1\right) \cos{\left(\pi n \right)}}{\pi n}$$
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
$$a_{n} = - \frac{\sin{\left(\pi n \right)} \cos{\left(\pi n \right)}}{2 \pi n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right) \left|{\frac{\sin{\left(\pi n \right)} \cos{\left(\pi n \right)}}{\sin{\left(\pi \left(n + 1\right) \right)} \cos{\left(\pi \left(n + 1\right) \right)}}}\right|}{n}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
0
$$0$$ 
0
The graph
Sum of series (-cos(n*(pi))/(n*(pi)))*(sen((n*(pi)))/2)

    Examples of finding the sum of a series

    © Mister Exam – Calculator