Sum of series 1/(n*(n-1))

The solution

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  oo           
 ___           
 \  `          
  \       1    
   )  ---------
  /   n*(n - 1)
 /__,          
n = 2

$$\sum_{n=2}^{\infty} \frac{1}{n \left(n - 1\right)}$$

Sum(1/(n*(n - 1)), (n, 2, oo))

The radius of convergence of the power series

Given number:
$$\frac{1}{n \left(n - 1\right)}$$
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
$$a_{n} = \frac{1}{n \left(n - 1\right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\left(n + 1\right) \left|{\frac{1}{n - 1}}\right|\right)$$
Let's take the limit
we find

True

False

The rate of convergence of the power series

The answer [src]

$$1$$

Numerical answer [src]

1.00000000000000000000000000000

1.00000000000000000000000000000

The graph

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```
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```
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```
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```
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```
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```
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```
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```
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```
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```
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```
Exam the series for convergence
```
(3*n - 1)/(-5)^n
```

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Sum of series 1/(n*(n-1))

The solution

Examples of finding the sum of a series