Mister Exam

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Sum of series:
t^k*(-1)^k*a^(2*k)*cos(a*x)*e^(a*z)/factorial(k)
a^n
5/(25*n^2-5*n-6)
tan(sqrt(n)/(n^2+1))
Identical expressions
one /((x)(x+ one)(x+ two))
1 divide by ((x)(x plus 1)(x plus 2))
one divide by ((x)(x plus one)(x plus two))
1/xx+1x+2
1 divide by ((x)(x+1)(x+2))
Similar expressions
1/((x)(x-1)(x+2))
1/(x*(x+1)*(x+2))
1/((x)(x+1)(x-2))

Sum of series/ 1/((x)(x+1)(x+2))

Sum of series 1/((x)(x+1)(x+2))

The solution

You have entered [src]

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

\sum_{x=1}^{\infty} \frac{1}{x \left(x + 1\right) \left(x + 2\right)}

Sum(1/((x*(x + 1))*(x + 2)), (x, 1, oo))

The radius of convergence of the power series

Given number:

\frac{1}{x \left(x + 1\right) \left(x + 2\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} = \frac{1}{x \left(x + 1\right) \left(x + 2\right)}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{x \to \infty}\left(\frac{x + 3}{x}\right)

Let's take the limit
we find

True

False

The rate of convergence of the power series

The answer [src]

1/4

\frac{1}{4}

1/4

Numerical answer [src]

0.250000000000000000000000000000

0.250000000000000000000000000000

The graph

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
```

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How to use it?

Identical expressions

Similar expressions

Sum of series 1/((x)(x+1)(x+2))

The solution

Examples of finding the sum of a series