SOLVED:Sometimes it's possible to use induction backwards, proving things from n to n-1 instead of vice versa! For example, consider the statement P(n): x1 …xn ⩽((x1+⋯+xn)/(n))^n, if x1, …, xn ⩾0 . This is true when n=2, since (x1+x2)^2-4 x1 x2=(x1-x2)^2 ⩾0. a By setting xn=(x1+⋯+xn-1) /(n-1), prove that P(n) implies P(n-1) whenever n>1. b Show that P(n) and P(2) imply P(2 n). c Explain why this implies the truth of P(n) for all n.
SOLVED:Sometimes it's possible to use induction backwards, proving …
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