Question

For non-negative integer n, let the function fn be given by (Picture)

 

(where n! = 1 · 2 · · · n, with the convention that 0! = 1, so that f0 (x) = 1, f1 (x) = 1 + x
etc.).
a) Show by induction that for non-negative integers n then f2n (x) is a positive number for
all real numbers x.

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