Let (P(n)) be the statement (2^{n}>n). (a) Show that (P(1)) is true. (b) Observe that if (2^{n}>n),

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 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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