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(sqrt(n)+1)/(n^3+5)

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  • Sum of series:
  • 2i 2i
  • 1/(n+1)! 1/(n+1)!
  • lnn/n lnn/n
  • factorial(n+2)/n^n factorial(n+2)/n^n

  • Identical expressions

  • (sqrt(n)+ one)/(n^ three + five)
  • ( square root of (n) plus 1) divide by (n cubed plus 5)
  • ( square root of (n) plus one) divide by (n to the power of three plus five)
  • (√(n)+1)/(n^3+5)
  • (sqrt(n)+1)/(n3+5)
  • sqrtn+1/n3+5
  • (sqrt(n)+1)/(n³+5)
  • (sqrt(n)+1)/(n to the power of 3+5)
  • sqrtn+1/n^3+5
  • (sqrt(n)+1) divide by (n^3+5)

  • Similar expressions

  • (sqrt(n)+1)/(n^3-5)
  • (sqrt(n)-1)/(n^3+5)
Sum of series/ (sqrt(n)+1)/(n^3+5)

Sum of series (sqrt(n)+1)/(n^3+5)


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The solution

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

False
The rate of convergence of the power series
Numerical answer [src] 
0.739926571791201834271929637053
0.739926571791201834271929637053
The graph
Sum of series (sqrt(n)+1)/(n^3+5)

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