Hello,
[tex]If\ n=1\ then\ 3^1 \geq 1+2^1\ since\ 3 \geq 3\\
\textrm{This proves the base case.}\\
\textrm{Now assume this holds for some n = k.}\\
\textrm{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.
[/tex]
