Find the following limit <munder> <mo movablelimits="true" form="prefix">lim <mrow clas

fythynwyrk0

fythynwyrk0

Answered question

2022-07-07

Find the following limit
lim N 1 N n = 1 N 1 n .

Answer & Explanation

Darrell Valencia

Darrell Valencia

Beginner2022-07-08Added 10 answers

By definition we know 0 1 f ( x ) d x = lim N 1 N n = 1 N f ( n N )
Also,
lim N 1 N n = 1 N 1 n = lim N 1 N n = 1 N N n = lim N 1 N n = 1 N f ( n N )
where f ( x ) = 1 x
Therefore:
lim N 1 N n = 1 N 1 n = 0 1 1 x d x = 2

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