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Sum of series:
1/(k*(k+1)*(k+2))
factorial(n+1)/n^n
1/((2n-1)(2n+3))
-1^(n-1)/((2*n-1)*3^(n-1))
Identical expressions
one /(k*(k+ one)*(k+ two))
1 divide by (k multiply by (k plus 1) multiply by (k plus 2))
one divide by (k multiply by (k plus one) multiply by (k plus two))
1/(k(k+1)(k+2))
1/kk+1k+2
1 divide by (k*(k+1)*(k+2))
Similar expressions
1/k(k+1)(k+2)
1/(k(k+1)(k+2))
1/(k*(k+1)*(k-2))
1/(k*(k-1)*(k+2))

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

The solution

You have entered [src]

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

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

Sum(1/((k*(k + 1))*(k + 2)), (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{1}{k \left(k + 1\right) \left(k + 2\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}{k \left(k + 1\right) \left(k + 2\right)}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty} 1

Let's take the limit
we find

True

False

The answer [src]

        oo       
-----------------
k*(1 + k)*(2 + k)

\frac{\infty}{k \left(k + 1\right) \left(k + 2\right)}

oo/(k*(1 + k)*(2 + k))

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/(k*(k+1)*(k+2))

The solution

Examples of finding the sum of a series

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