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Ever noticed that the coefficients in (1+x)⁴ — that's 1, 4, 6, 4, 1 — form a perfect mirror? It works for every single power of n, and there's a deep reason why. In this short, we prove that the coefficient of the (r+1)th term from the start equals the coefficient of the (r+1)th term from the end — because ⁿCr = ⁿC(n−r), always ...
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