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-(16/2^n)*n

Sum of series -(16/2^n)*n



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The solution

You have entered [src]
  oo       
 ___       
 \  `      
  \     n  
  /   -8 *n
 /__,      
n = 1      
$$\sum_{n=1}^{\infty} - 8^{n} n$$
Sum((-8^n)*n, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$- 8^{n} n$$
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
$$a_{n} = - n$$
and
$$x_{0} = -8$$
,
$$d = 1$$
,
$$c = 0$$
then
$$R = \tilde{\infty} \left(-8 + \lim_{n \to \infty}\left(\frac{n}{n + 1}\right)\right)$$
Let's take the limit
we find
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 -(16/2^n)*n

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