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2(1/(n^2+5n+6))

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  • Sum of series:
  • 3i
  • n^2*x^n
  • n^3 n^3
  • 2(1/(n^2+5n+6)) 2(1/(n^2+5n+6))

  • Identical expressions

  • two (one /(n^ two +5n+ six))
  • 2(1 divide by (n squared plus 5n plus 6))
  • two (one divide by (n to the power of two plus 5n plus six))
  • 2(1/(n2+5n+6))
  • 21/n2+5n+6
  • 2(1/(n²+5n+6))
  • 2(1/(n to the power of 2+5n+6))
  • 21/n^2+5n+6
  • 2(1 divide by (n^2+5n+6))

  • Similar expressions

  • 2(1/(n^2+5n-6))
  • 2(1/(n^2-5n+6))
Sum of series/ 2(1/(n^2+5n+6))

Sum of series 2(1/(n^2+5n+6))


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The solution

You have entered [src] 
  oo              
____              
\   `             
 \         2      
  \   ------------
  /    2          
 /    n  + 5*n + 6
/___,             
n = 0
$$\sum_{n=0}^{\infty} \frac{2}{\left(n^{2} + 5 n\right) + 6}$$ 
Sum(2/(n^2 + 5*n + 6), (n, 0, oo))
The radius of convergence of the power series
Given number:
$$\frac{2}{\left(n^{2} + 5 n\right) + 6}$$
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
$$a_{n} = \frac{2}{n^{2} + 5 n + 6}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{2 \left(\frac{5 n}{2} + \frac{\left(n + 1\right)^{2}}{2} + \frac{11}{2}\right)}{n^{2} + 5 n + 6}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
1
$$1$$ 
1
Numerical answer [src] 
1.00000000000000000000000000000
1.00000000000000000000000000000
The graph
Sum of series 2(1/(n^2+5n+6))

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