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sqrt((1+5*n)/n)

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  • Sum of series:
  • x^n/n
  • n^2/3^n n^2/3^n
  • (2^n+(-1)^n)/5^n (2^n+(-1)^n)/5^n
  • 1/n^6 1/n^6

  • Identical expressions

  • sqrt((one + five *n)/n)
  • square root of ((1 plus 5 multiply by n) divide by n)
  • square root of ((one plus five multiply by n) divide by n)
  • √((1+5*n)/n)
  • sqrt((1+5n)/n)
  • sqrt1+5n/n
  • sqrt((1+5*n) divide by n)

  • Similar expressions

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

Sum of series sqrt((1+5*n)/n)


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The solution

You have entered [src] 
  oo               
____               
\   `              
 \        _________
  \      / 1 + 5*n 
  /     /  ------- 
 /    \/      n    
/___,              
n = 1
$$\sum_{n=1}^{\infty} \sqrt{\frac{5 n + 1}{n}}$$ 
Sum(sqrt((1 + 5*n)/n), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\sqrt{\frac{5 n + 1}{n}}$$
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
$$a_{n} = \sqrt{\frac{5 n + 1}{n}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\sqrt{n + 1} \sqrt{5 n + 1}}{\sqrt{n} \sqrt{5 n + 6}}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
  oo             
____             
\   `            
 \      _________
  \   \/ 1 + 5*n 
   )  -----------
  /        ___   
 /       \/ n    
/___,            
n = 1
$$\sum_{n=1}^{\infty} \frac{\sqrt{5 n + 1}}{\sqrt{n}}$$ 
Sum(sqrt(1 + 5*n)/sqrt(n), (n, 1, oo))
The graph
Sum of series sqrt((1+5*n)/n)

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