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exp^(n^2)

  • How to use it?

  • Sum of series:
  • n^2 n^2
  • exp^(n^2) exp^(n^2)
  • ln(n)/n ln(n)/n
  • sin(1/k)

  • 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

You have entered [src] 
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n = 1
∑n=1∞en2\sum_{n=1}^{\infty} e^{n^{2}} 
Sum(E^(n^2), (n, 1, oo))
The radius of convergence of the power series
Given number:
en2e^{n^{2}}
It is a series of species
an(cx−x0)dna_{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:
Rd=x0+lim⁡n→∞∣anan+1∣cR^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}
In this case
an=en2a_{n} = e^{n^{2}}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=lim⁡n→∞(en2e−(n+1)2)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
1.07.01.52.02.53.03.54.04.55.05.56.06.502e21
The answer [src] 
  oo       
 ___       
 \  `      
  \    / 2\
   )   \n /
  /   e    
 /__,      
n = 1
∑n=1∞en2\sum_{n=1}^{\infty} e^{n^{2}} 
Sum(exp(n^2), (n, 1, oo))
The graph
Sum of series exp^(n^2)

    Examples of finding the sum of a series

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