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Start with the formula in the binomial theorem. Plug in y = 1 and differentiate. Multiply the result by x and differentiate again. Finally,

Start with the formula in the binomial theorem. Plug in y = 1 and differentiate. Multiply the result by x and differentiate again. Finally, plug in x = 1. What identity have you proven. Pick either side of what you have proven and give a combinatorial situation it counts.

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By starting with the formula in the binomial theorem and plugging in y 1 we have 1 xn Cn0 Cn1x Cn2x2 ... blur-text-image

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