Question: Let (P(n)) be the statement (2^{n}>n). (a) Show that (P(1)) is true. (b) Observe that if (2^{n}>n), then (2^{n}+2^{n}>2 n). Use this to show that
Let \(P(n)\) be the statement \(2^{n}>n\).
(a) Show that \(P(1)\) is true.
(b) Observe that if \(2^{n}>n\), then \(2^{n}+2^{n}>2 n\). Use this to show that if \(P(n)\) is true for \(n=k\), then \(P(n)\) is true for \(n=k+1\). Conclude that \(P(n)\) is true for all \(n\).
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