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(n^11)^3:(n^5)^2

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  • Sum of series:
  • 20 20
  • (n^11)^3:(n^5)^2 (n^11)^3:(n^5)^2
  • f(x)
  • 1/sqrt(n) 1/sqrt(n)

  • Identical expressions

  • (n^ eleven)^ three :(n^ five)^ two
  • (n to the power of 11) cubed :(n to the power of 5) squared
  • (n to the power of eleven) to the power of three :(n to the power of five) to the power of two
  • (n11)3:(n5)2
  • n113:n52
  • (n^11)³:(n⁵)²
  • (n to the power of 11) to the power of 3:(n to the power of 5) to the power of 2
  • n^11^3:n^5^2
Sum of series/ (n^11)^3:(n^5)^2

Sum of series (n^11)^3:(n^5)^2


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The solution

You have entered [src] 
  oo         
_____        
\    `       
 \          3
  \    / 11\ 
   \   \n  / 
    )  ------
   /       2 
  /    / 5\  
 /     \n /  
/____,       
n = 1
$$\sum_{n=1}^{\infty} \frac{\left(n^{11}\right)^{3}}{\left(n^{5}\right)^{2}}$$ 
Sum((n^11)^3/(n^5)^2, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\left(n^{11}\right)^{3}}{\left(n^{5}\right)^{2}}$$
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
$$a_{n} = n^{23}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{n^{23}}{\left(n + 1\right)^{23}}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
oo
$$\infty$$ 
oo
Numerical answer
The series diverges
The graph
Sum of series (n^11)^3:(n^5)^2

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