ok look at it this way..
PMI= if f(a), where a is some constant, is true for statement, then f(k) is true, from there if f(k+1) is true, the statement it true
F(2) is what? 22-1<(2)!, 21=1<2=2!
this is true, so it follows that f(k) is true!
then we assume 2k-1<k!
now we need to...