Mister Exam

Sum of series 0.5



=

The solution

You have entered [src]
  oo      
 __       
 \ `      
  )    1/2
 /_,      
n = 10    
$$\sum_{n=10}^{\infty} \frac{1}{2}$$
Sum(1/2, (n, 10, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{2}$$
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
$$a_{n} = \frac{1}{2}$$
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 rate of convergence of the power series
The answer [src]
oo
$$\infty$$
oo
Numerical answer
The series diverges
The graph
Sum of series 0.5

    Examples of finding the sum of a series