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sqrt((n+1)/n)
Sum of series/ sqrt((n+1)/n)

Sum of series sqrt((n+1)/n)


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The solution

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

False
The rate of convergence of the power series
The answer [src] 
  oo           
____           
\   `          
 \      _______
  \   \/ 1 + n 
   )  ---------
  /       ___  
 /      \/ n   
/___,          
n = 1
$$\sum_{n=1}^{\infty} \frac{\sqrt{n + 1}}{\sqrt{n}}$$ 
Sum(sqrt(1 + n)/sqrt(n), (n, 1, oo))
The graph
Sum of series sqrt((n+1)/n)

    Examples of finding the sum of a series

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