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Sum of first n odd numbers | Visual mathematics |
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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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Support my animations on:
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Any further questions or ideas:
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Overall render time: ~ 8 hours
Programs used:
- Cinema 4D (3D animation)
_________________________________________________________________
Music:
CLAUDE DEBUSSY: CLAIR DE LUNE
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.
Subscribe for more:)
_________________________________________________________________
Support my animations on:
_________________________________________________________________
Any further questions or ideas:
_________________________________________________________________
Overall render time: ~ 8 hours
Programs used:
- Cinema 4D (3D animation)
_________________________________________________________________
Music:
CLAUDE DEBUSSY: CLAIR DE LUNE
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