Mister Exam

Sum of series yi



=

The solution

You have entered [src]
  oo     
 __      
 \ `     
  )   y*i
 /_,     
i = 1    
$$\sum_{i=1}^{\infty} i y$$
Sum(y*i, (i, 1, oo))
The radius of convergence of the power series
Given number:
$$i y$$
It is a series of species
$$a_{i} \left(c y - y_{0}\right)^{d i}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{y_{0} + \lim_{i \to \infty} \left|{\frac{a_{i}}{a_{i + 1}}}\right|}{c}$$
In this case
$$a_{i} = i y$$
and
$$y_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{i \to \infty}\left(\frac{i}{i + 1}\right)$$
Let's take the limit
we find
True

False
The answer [src]
oo*y
$$\infty y$$
oo*y

    Examples of finding the sum of a series