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bonzini
6 months ago
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Happy New Year 2025
The sum of the first n cubes is always the square of the sum of numbers from 1 to n. For example 1³+2³+3³+4³=(1+2+3+4)².
You can prove it by induction; just expand (n(n+1)/2)² – (n(n-1)/2)², the result is n³.
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You can prove it by induction; just expand (n(n+1)/2)² – (n(n-1)/2)², the result is n³.