SOLUTION: Prove using induction that: for every non negative integer n, 2^n>n

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Question 1022311: Prove using induction that: for every non negative integer n, 2^n>n
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
For n = 1: 2%5E1+%3E+1, which is true
Assume for n = k>1 that 2%5Ek+%3E+k.
Show that the hypothesis is true also for n = k + 1, or that 2%5E%28k%2B1%29+%3Ek%2B1.
But 2%5E%28k%2B1%29+=+2%5Ek%2A2+%3E2k+=+k%2Bk%3Ek%2B1, and the statement is proved.