I want to find the limit of the given series: <munder> <mo movablelimits="true" form="prefix

Lovellss

Lovellss

Answered question

2022-06-14

I want to find the limit of the given series:
lim n 1 2022 + 2 2022 + . . . + n 2022 n

Answer & Explanation

scipionhi

scipionhi

Beginner2022-06-15Added 25 answers

Yes, your bounds work: in particular, for every positive integer n
n 2022 1 2022 + 2 2022 + + n 2022 n 2022 + n 2022 + + n 2022 n  times = n 2023 .
While a tighter lower bound can be obtained via the AM-GM inequality,
1 2022 + 2 2022 + + n 2022 n ( n ! ) 2022 / n ,
it doesn't actually make the problem any easier, since we would have to show
lim n ( n ! ) 1 / n 2 = 1.

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