Mister Exam

Other calculators

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

Sum of series 1/sqrt(n)


∑
=

The solution

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

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

    Examples of finding the sum of a series

    © Mister Exam – Calculator