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(4i+5)/10^2
Sum of series/ (4i+5)/10^2

Sum of series (4i+5)/10^2


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The solution

You have entered [src] 
  oo         
 ___         
 \  `        
  \   4*i + 5
   )  -------
  /     100  
 /__,        
i = 1
$$\sum_{i=1}^{\infty} \frac{4 i + 5}{100}$$ 
Sum((4*i + 5)/100, (i, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{4 i + 5}{100}$$
It is a series of species
$$a_{i} \left(c x - x_{0}\right)^{d i}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{i \to \infty} \left|{\frac{a_{i}}{a_{i + 1}}}\right|}{c}$$
In this case
$$a_{i} = \frac{i}{25} + \frac{1}{20}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{i \to \infty}\left(\frac{\frac{i}{25} + \frac{1}{20}}{\frac{i}{25} + \frac{9}{100}}\right)$$
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 (4i+5)/10^2

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