2025-02-25 09:26 UTC
@pfsmet@mastodon.social is it common to have sum(N) { i³ } = (sum(N) { i })², by the way ?
Replies (1)
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@pfsmet@mastodon.social 2025-02-26 20:06
@PypeBros@mastodon.social It always holds, for any n! The sum of cubes from 1³ to n³ can be expressed as n²(n+1)²/4. This is the same as (n(n+1)/2)². The sum of the first n positive integers is expressed as n(n+1)/2 (n numbers times the average of first and last, (n+1)/2. So, if you square the last expression, you get the other expression. ☐