How to calculate lim_(n => infty) (1-(1)/(x^n))^n ?

brasocas6

brasocas6

Answered question

2022-08-09

How to calculate lim n ( 1 1 x n ) n , x > 1 ?

Answer & Explanation

Dereon Parker

Dereon Parker

Beginner2022-08-10Added 11 answers

We can use
lim n ( 1 1 n ) n = e 1 .
Also, recall that
lim n n x n = 0 ,  if  x > 1.
So
( 1 1 x n ) n = ( 1 1 x n ) x n x n n = ( 1 1 x n ) x n n x n = ( ( 1 1 x n ) x n ) n x n n ( e 1 ) 0 = 1.

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