Mister Exam

# Sum of series f(x)

=

### The solution

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

False
oo*f
$$\infty f$$
oo*f`