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1/4+1/28+1/70

Sum of series 1/4+1/28+1/70



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The solution

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  oo                     
 __                      
 \ `                     
  )   (1/4 + 1/28 + 1/70)
 /_,                     
n = 1                    
$$\sum_{n=1}^{\infty} \left(\frac{1}{70} + \left(\frac{1}{28} + \frac{1}{4}\right)\right)$$
Sum(1/4 + 1/28 + 1/70, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{70} + \left(\frac{1}{28} + \frac{1}{4}\right)$$
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
$$a_{n} = \frac{3}{10}$$
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 1/4+1/28+1/70

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