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n^2*exp(-(n)^1/2)

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  • Sum of series:
  • (-1)^n*sqrt(n)/(n+100) (-1)^n*sqrt(n)/(n+100)
  • n^2*x^n
  • 2(1/(n^2+5n+6)) 2(1/(n^2+5n+6))
  • ((-1)^n)*((x^n)/(2n*n!))

  • Identical expressions

  • n^ two *exp(-(n)^ one / two)
  • n squared multiply by exponent of ( minus (n) to the power of 1 divide by 2)
  • n to the power of two multiply by exponent of ( minus (n) to the power of one divide by two)
  • n2*exp(-(n)1/2)
  • n2*exp-n1/2
  • n²*exp(-(n)^1/2)
  • n to the power of 2*exp(-(n) to the power of 1/2)
  • n^2exp(-(n)^1/2)
  • n2exp(-(n)1/2)
  • n2exp-n1/2
  • n^2exp-n^1/2
  • n^2*exp(-(n)^1 divide by 2)

  • Similar expressions

  • n^2*exp((n)^1/2)
Sum of series/ n^2*exp(-(n)^1/2)

Sum of series n^2*exp(-(n)^1/2)


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The solution

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

False
The rate of convergence of the power series
Numerical answer [src] 
239.994930345328242743435897448
239.994930345328242743435897448
The graph
Sum of series n^2*exp(-(n)^1/2)

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