Mister Exam

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Sum of series:
6/9n^2+12n-5
5^n
1/(3n+1)(3n+4)
(3-sin*n)/n-lnn
Graphing y =:
1/(x(x+1))
Integral of d{x}:
1/(x(x+1))
Identical expressions
one /(x(x+ one))
1 divide by (x(x plus 1))
one divide by (x(x plus one))
1/xx+1
1 divide by (x(x+1))
Similar expressions
1/((x)(x+1)(x+2))
1/(x(x-1))
1/(x*(x+1)*(x+2))

Sum of series 1/(x(x+1))

The solution

You have entered [src]

  oo           
 ___           
 \  `          
  \       1    
   )  ---------
  /   x*(x + 1)
 /__,          
k = 1

$$\sum_{k=1}^{\infty} \frac{1}{x \left(x + 1\right)}$$

Sum(1/(x*(x + 1)), (k, 1, oo))

The radius of convergence of the power series

Given number:
$$\frac{1}{x \left(x + 1\right)}$$
It is a series of species
$$a_{k} \left(c x - x_{0}\right)^{d k}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{k \to \infty} \left|{\frac{a_{k}}{a_{k + 1}}}\right|}{c}$$
In this case
$$a_{k} = \frac{1}{x \left(x + 1\right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{k \to \infty} 1$$
Let's take the limit
we find

True

False

The answer [src]

    oo   
---------
x*(1 + x)

$$\frac{\infty}{x \left(x + 1\right)}$$

oo/(x*(1 + x))

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
```

Other calculators

How to use it?

Identical expressions

Similar expressions

Sum of series 1/(x(x+1))

The solution

Examples of finding the sum of a series