I would like to evaluate: lim n → ∞ 1 n 3 ∑ ℓ =...

vrotterigzl

vrotterigzl

Answered

2022-06-24

I would like to evaluate:
lim n 1 n 3 = 1 n 1 ( n 2 2 ) ( n 2 ( 1 ) 2 )

Answer & Explanation

Zayden Andrade

Zayden Andrade

Expert

2022-06-25Added 22 answers

For every 1 n 1
n 2 2 ( n 2 2 ) ( n 2 ( 1 ) 2 ) n 2 ( 1 ) 2 ,
hence the sums S n you are interested in are such that R n S n T n for every n 1, with
R n = 1 n 3 = 1 n 1 ( n 2 2 ) , T n = 1 n 3 = 0 n 2 ( n 2 2 ) .
The rest should be easy (and the limit is indeed 2 3 )

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