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18/(n^2-7*n+10)

  • How to use it?

  • Sum of series:
  • (3^n-1)/6^n (3^n-1)/6^n
  • 18/(n^2-7*n+10) 18/(n^2-7*n+10)
  • ln(5k/n)
  • 150 150

  • Identical expressions

  • eighteen /(n^ two - seven *n+ ten)
  • 18 divide by (n squared minus 7 multiply by n plus 10)
  • eighteen divide by (n to the power of two minus seven multiply by n plus ten)
  • 18/(n2-7*n+10)
  • 18/n2-7*n+10
  • 18/(n²-7*n+10)
  • 18/(n to the power of 2-7*n+10)
  • 18/(n^2-7n+10)
  • 18/(n2-7n+10)
  • 18/n2-7n+10
  • 18/n^2-7n+10
  • 18 divide by (n^2-7*n+10)

  • Similar expressions

  • 18/(n^2+7*n+10)
  • 18/(n^2-7*n-10)
Sum of series/ 18/(n^2-7*n+10)

Sum of series 18/(n^2-7*n+10)


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The solution

You have entered [src] 
  oo               
____               
\   `              
 \          18     
  \   -------------
  /    2           
 /    n  - 7*n + 10
/___,              
n = 7
$$\sum_{n=7}^{\infty} \frac{18}{\left(n^{2} - 7 n\right) + 10}$$ 
Sum(18/(n^2 - 7*n + 10), (n, 7, oo))
The radius of convergence of the power series
Given number:
$$\frac{18}{\left(n^{2} - 7 n\right) + 10}$$
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
$$a_{n} = \frac{18}{n^{2} - 7 n + 10}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(18 \left|{\frac{- \frac{7 n}{18} + \frac{\left(n + 1\right)^{2}}{18} + \frac{1}{6}}{n^{2} - 7 n + 10}}\right|\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
  /        0\     /        0\
3*\-5 + 3*e /   6*\-1 + 2*e /
------------- + -------------
          0               0  
  -6 + 6*e        -6 + 6*e
$$\frac{3 \left(-5 + 3 e^{0}\right)}{-6 + 6 e^{0}} + \frac{6 \left(-1 + 2 e^{0}\right)}{-6 + 6 e^{0}}$$ 
3*(-5 + 3*exp_polar(0))/(-6 + 6*exp_polar(0)) + 6*(-1 + 2*exp_polar(0))/(-6 + 6*exp_polar(0))
Numerical answer [src] 
6.50000000000000000000000000000
6.50000000000000000000000000000
The graph
Sum of series 18/(n^2-7*n+10)

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