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sqrt(1+5n/n)

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



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The solution

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

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