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exp^(n^2)

  • How to use it?

  • Sum of series:
  • (3^n+5^n)/15^n (3^n+5^n)/15^n
  • (3^n+2^n)/6^n (3^n+2^n)/6^n
  • sin(1/n)/sqrt(n) sin(1/n)/sqrt(n)
  • lnx lnx

  • Identical expressions

  • exp^(n^ two)
  • exponent of to the power of (n squared )
  • exponent of to the power of (n to the power of two)
  • exp(n2)
  • expn2
  • exp^(n²)
  • exp to the power of (n to the power of 2)
  • exp^n^2
Sum of series/ exp^(n^2)

Sum of series exp^(n^2)


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The solution

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n = 1
$$\sum_{n=1}^{\infty} e^{n^{2}}$$ 
Sum(E^(n^2), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$e^{n^{2}}$$
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
$$a_{n} = e^{n^{2}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(e^{n^{2}} e^{- \left(n + 1\right)^{2}}\right)$$
Let's take the limit
we find
False

False
The rate of convergence of the power series
The answer [src] 
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  \    / 2\
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n = 1
$$\sum_{n=1}^{\infty} e^{n^{2}}$$ 
Sum(exp(n^2), (n, 1, oo))
The graph
Sum of series exp^(n^2)

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