perplexus.info :: Just Math : Cube Rooted and Squared Til 2023

Cube Rooted and Squared Til 2023 (Posted on 2023-02-08)

Determine ⌈N⌉, when it is known that:

       1         1                1
N = ------- + ------- + ... + ---------- 
    ⌈(1)^2/3⌉   ⌈(2)^2/3⌉        ⌈(2023)^2/3⌉

Note: ⌈p⌉ is the ceiling of p, which is equal to the least integer greater than or equal to p.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

computer evaluation (spoiler)

| Comment 1 of 2

N=0;

for i=1:2023

N=N+1/ ceil((i)^(2/3));

end

finds

N =

34.5046741171236

so the sought ceiling of N is 35.

Posted by Charlie on 2023-02-08 09:38:08

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