Think Twice | Sum of first n odd numbers | Visual mathematics | @ThinkTwiceLtu | Uploaded July 2017 | Updated October 2024, 1 day ago.
Short animation about the sum of first n odd numbers.

here is an algebraic proof:

The first n odd natural numbers are 1, 3, 5, ... 2n-1. This forms an arithmetic progression with first term 1, common difference 2 and last term (2n-1).

The sum is given by S = 1+3+5+...+(2n-1).
Using S = n (First term + Last term)/2,
we get S = n (1+2n-1)/2,
which simplifies to S = n^2.

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Overall render time: ~ 8 hours

Programs used:

- Cinema 4D (3D animation)

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Music:

CLAUDE DEBUSSY: CLAIR DE LUNE