Mister Exam

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Sum of series:
1/((2n-1)*(2n+1))
(-1/2)^n
sin1/n
1/(n(n+2)(n+1))
Integral of d{x}:
x(x-1)
Graphing y =:
x(x-1)
Identical expressions
x(x- one)
x(x minus 1)
x(x minus one)
xx-1
Similar expressions
2^2x*(x-1/4)x
5^(nx)*atan(x/(7^(n*x)*(x-1)))
x*(x-1)
x(x+1)
2^2x(x-1/4)x
2^(2x)(x-1/4)x

Sum of series/ x(x-1)

Sum of series x(x-1)

The solution

You have entered [src]

  oo           
 __            
 \ `           
  )   x*(x - 1)
 /_,           
x = 1

\sum_{x=1}^{\infty} x \left(x - 1\right)

Sum(x*(x - 1), (x, 1, oo))

The radius of convergence of the power series

Given number:

x \left(x - 1\right)

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} = x \left(x - 1\right)

and

x_{0} = 0

,

d = 0

,

c = 1

then

1 = \lim_{x \to \infty}\left(\frac{\left|{x - 1}\right|}{x + 1}\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 x(x-1)

Examples of finding the sum of a series

The Sum of the Power Series
```
x^n/n
```
```
(x-1)^n
```
Factorial
```
1/2^(n!)
```
```
n^2/n!
```
```
x^n/n!
```
```
k!/(n!*(n+k)!)
```
Flint Hills Series
```
csc(n)^2/n^3
```
Basel problem
```
1/n^2
```
```
1/n^4
```
```
1/n^6
```
Harmonic series
```
1/n
```
Grandi's series
```
(-1)^n
```
Alternating series
```
(-1)^(n + 1)/n
```
```
(n + 2)*(-1)^(n - 1)
```
```
(3*n - 1)/(-5)^n
```
```
(-1)^(n - 1)*n/(6*n - 5)
```
Newton–Mercator series
```
(-1)^(n + 1)/n*x^n
```
Exam the series for convergence
```
(3*n - 1)/(-5)^n
```