You can
put this solution on YOUR website!The induction basically claims that if for some k > 1, if
, then
^2)
.
Since
 \ge 2k^2)
, we can construct the inequality
^2)
The inequality
^2)
is equivalent to
It factors to
^2 - 2 \ge 0 \Rightarrow (k-1)^2 \ge 2)
, which is true for sufficiently large k (it doesn't hold for k = 0,1,2 but we can check these cases separately).
