Prove by PMI that
3^n >= 1+2^n

ANSWERS

2015-11-01 12:43:49

Hello, [latex]If n=1 then 3^1 geq 1+2^1 since 3 geq 3\ extrm{This proves the base case.}\ extrm{Now assume this holds for some n = k.}\ extrm{We need to show this holds for n = k +1}\ 3^k geq 1+2^k is true.\ 3^{k+1}=3*3^k geq 3*(1+2^k)\ 3^{k+1}=3+(1+2)*2^k=3+2^k+2^{k+1} geq 3+2^{k+1}\ 3^{k+1} geq 1+2^{k+1} is true. [/latex]

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