@3blue1brown recently made a nice animation for this:https://twitter.com/3blue1brown/status/1022544780092354560 …
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Nitpicking, but I'd consider this more of a visual proof for n*(n+1)/2 and not n^2/2 + n/2. I interpret the former as half of the area of a single rectangle with sides n, n+1. The latter expresses the addition of two shapes which is what is in the picture
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Exercise: Extend this approach to show that 1 + 2² + 3² + ... + n² = (2n³+3n²+n)/6. What about 1 + 2³ + 3³ + ... + n³?
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Here's a great visual proof of the sum of squares:https://twitter.com/NathanielRaley/status/476848567122796544 …
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Also, another easy way to remember: 2 x Sum[1..n] = 1, 2, 3, ... n n, n-1, n-2, ... 1 + ----------------------- n+1, n+1, n+1, ... n+1 = n(n+1) So Sum[1..n] = n(n+1) / 2
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For some dim weird I like me, let me put it this way 2*(1+2+3+...+n) = n^2+n
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This is cool :)
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Very. I am going to print this and use it in my room during summers
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More easily observed as 2 * (1+2+3+...+n) at the top and n^2 + n at the bottom
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Indeed. Left as an exercise for the reader.
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