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1/n(n-1)

Sum of series 1/n(n-1)



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The solution

You have entered [src]
  oo       
 ___       
 \  `      
  \   n - 1
   )  -----
  /     n  
 /__,      
n = 2      
$$\sum_{n=2}^{\infty} \frac{n - 1}{n}$$
Sum((n - 1)/n, (n, 2, oo))
The radius of convergence of the power series
Given number:
$$\frac{n - 1}{n}$$
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
$$a_{n} = \frac{n - 1}{n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right) \left|{n - 1}\right|}{n^{2}}\right)$$
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 1/n(n-1)

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