Mister Exam

Other calculators

sqrt(n^3+2)/(n^2+3)

  • How to use it?

  • Sum of series:
  • (-1)^n (-1)^n
  • sqrt(n^3+2)/(n^2+3) sqrt(n^3+2)/(n^2+3)
  • 17 17
  • ((8)(ln(x)))/(x^3)

  • Identical expressions

  • sqrt(n^ three + two)/(n^ two + three)
  • square root of (n cubed plus 2) divide by (n squared plus 3)
  • square root of (n to the power of three plus two) divide by (n to the power of two plus three)
  • √(n^3+2)/(n^2+3)
  • sqrt(n3+2)/(n2+3)
  • sqrtn3+2/n2+3
  • sqrt(n³+2)/(n²+3)
  • sqrt(n to the power of 3+2)/(n to the power of 2+3)
  • sqrtn^3+2/n^2+3
  • sqrt(n^3+2) divide by (n^2+3)

  • Similar expressions

  • sqrt(n^3+2)/(n^2-3)
  • sqrt(n^3-2)/(n^2+3)
Sum of series/ sqrt(n^3+2)/(n^2+3)

Sum of series sqrt(n^3+2)/(n^2+3)


∑
=

The solution

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

False
The rate of convergence of the power series
Numerical answer
The series diverges
The graph
Sum of series sqrt(n^3+2)/(n^2+3)

    Examples of finding the sum of a series

    © Mister Exam – Calculator