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  • Sum of series:
  • 1/(3n-2)*(3n+1) 1/(3n-2)*(3n+1)
  • 1/ln(n) 1/ln(n)
  • 14/(49n^2-70n-24) 14/(49n^2-70n-24)
  • sqrt((k*x^2)/m)

  • Identical expressions

  • sqrt((k*x^ two)/m)
  • square root of ((k multiply by x squared ) divide by m)
  • square root of ((k multiply by x to the power of two) divide by m)
  • √((k*x^2)/m)
  • sqrt((k*x2)/m)
  • sqrtk*x2/m
  • sqrt((k*x²)/m)
  • sqrt((k*x to the power of 2)/m)
  • sqrt((kx^2)/m)
  • sqrt((kx2)/m)
  • sqrtkx2/m
  • sqrtkx^2/m
  • sqrt((k*x^2) divide by m)
Sum of series/ sqrt((k*x^2)/m)

Sum of series sqrt((k*x^2)/m)


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The solution

You have entered [src] 
  oo             
____             
\   `            
 \         ______
  \       /    2 
   )     /  k*x  
  /     /   ---- 
 /    \/     m   
/___,            
n = 1
$$\sum_{n=1}^{\infty} \sqrt{\frac{k x^{2}}{m}}$$ 
Sum(sqrt((k*x^2)/m), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\sqrt{\frac{k x^{2}}{m}}$$
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
$$a_{n} = \sqrt{\frac{k x^{2}}{m}}$$
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 answer [src] 
        ______
       /    2 
      /  k*x  
oo*  /   ---- 
   \/     m
$$\infty \sqrt{\frac{k x^{2}}{m}}$$ 
oo*sqrt(k*x^2/m)

    Examples of finding the sum of a series

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