Hello, I am having some trouble with the following proofs by induction. I understand how to get the base case and induction hypothesis but its the actual induction that's bothering me. Sorry that it looks ugly but this is my first post and I haven't been able to figure out the formatting codes yet.
1.) 2^n >= 1/8 n >= -3
2.) (3/2)^n >= (1+ n/2) n>=1
for 1 tried 2^(n+1) = 2*2^n >= 2*(1/8) > 1/8
This however does not preserve the >=, just >. This makes sense to me on an instinctual level because n>= -3 means that n+1 will always be greater than 1/8
for 2 I tried 1+(n+1)/2 = 1 + n/2 + 1/2 <= (3/2)^n + 1/2 < (3/2)^(n+1) but again this did not preserve <= but just <.