Question

e escribe los primeros 20 terminos de la sucesión de Euler an- (1+1/n)n
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Answer 1

Explicación

an- (1+1/n)n

(1+1/1)^2=2. Then, 1/(e - 2) = 1.3922...

(1+1/2)^2= 2.25. Then, (1/e-2.25) = 2.1355...

n = 250

todo da 0

ya que

(1+x)=x−x22+o(x2) x=1+x+o(x)  x→0.

(1+1n)n=enln(1+1n)=en(1n−12n2+o(1n2))=e1−12n+o(1n)=e⋅e−12n+o(1n)=e⋅(1−12n+o(1n))=e−e2n+o(1n)

(1+1n)n−e∼n→∞−e2n.