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Mathematics, 27.11.2019 03:31 delincuent5641

Let c(n) be the constant term in the expansion of (x + 4)n. prove by induction that c(n) = 4n for all n is in n. (induction on n.) the constant term of (x + 4)1 is = 4 . suppose as inductive hypothesis that the constant term of (x + 4)k − 1 is for some k > 1. then (x + 4)k = (x + 4)k − 1 · , so its constant term is · 4 = , as required.

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