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Some Even and Odd Crossed Difference (Posted on 2023-11-03)

Let M = sum of the cubes of the first 2024 odd numbers
and N = sum of the cubes of the first 2023 even numbers.

Find M-N

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Possible Solution

| Comment 1 of 3

Sums of odd and even cubes, up to n:

n^2(2n^2-1) (odd)

2n^2(n+1)^2 (even)

So, for (n-1) even numbers: 2(n-1)^2n^2

Deducting:

n^2(2n^2-1)-2(n-1)^2n^2

=n^2((2n^2-1)-2(n-1)^2), when (2n^2-1)-2(n-1)^2=(4n-3)

=n^2(4n-3)

Let n=2024 then n^2(4n-3) = 33,153,589,568

Posted by broll on 2023-11-03 07:20:52

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