Mister Exam

Other calculators

n*exp(-n^2)

  • How to use it?

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

  • Identical expressions

  • n*exp(-n^ two)
  • n multiply by exponent of ( minus n squared )
  • n multiply by exponent of ( minus n to the power of two)
  • n*exp(-n2)
  • n*exp-n2
  • n*exp(-n²)
  • n*exp(-n to the power of 2)
  • nexp(-n^2)
  • nexp(-n2)
  • nexp-n2
  • nexp-n^2

  • Similar expressions

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

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


∑
=

The solution

You have entered [src] 
  oo        
 ___        
 \  `       
  \        2
   )     -n 
  /   n*e   
 /__,       
n = 1
∑n=1∞ne−n2\sum_{n=1}^{\infty} n e^{- n^{2}} 
Sum(n*exp(-n^2), (n, 1, oo))
The radius of convergence of the power series
Given number:
ne−n2n e^{- 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=ne−n2a_{n} = n e^{- n^{2}}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=lim⁡n→∞(ne−n2e(n+1)2n+1)1 = \lim_{n \to \infty}\left(\frac{n e^{- n^{2}} e^{\left(n + 1\right)^{2}}}{n + 1}\right)
Let's take the limit
we find
False

False
The rate of convergence of the power series
1.07.01.52.02.53.03.54.04.55.05.56.06.50.350.45
Numerical answer [src] 
0.404881398571310708910099048243
0.404881398571310708910099048243
The graph
Sum of series n*exp(-n^2)

    Examples of finding the sum of a series

    © Mister Exam – Calculator