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lim-x-1-n-




Question Number 131938 by Raxreedoroid last updated on 09/Feb/21
lim_(x→∞) (1/( (√(n!))))=?
limx1n!=?
Answered by Faetma last updated on 09/Feb/21
 {: ((lim_(n→+∞)  n!=+∞)),((lim_(N→+∞)  (√N)=+∞)),((lim_(N′→+∞)  (1/(N′))=0^+ )) }lim_(n→+∞)  (1/( (√(n!))))=0^+
limn+n!=+limN+N=+limN+1N=0+}limn+1n!=0+
Answered by Eyass last updated on 10/Feb/21
∀n∈N ; n! > n  ⇔         , (√(n!))>(√n)  ⇒ n∈N^∗ , 0<(1/( (√(n!)))) < (1/( (√n)))  lim_(n→+∞)  ((1/( (√n)))) = 0 ⇒ lim_(n→+∞)  ((1/( (√(n!))))) = 0
nN;n!>n,n!>nnN,0<1n!<1nlimn+(1n)=0limn+(1n!)=0

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