1.  Do some algebra based on the previous hint and show a_m = [ sqrt(2m) + 1/2 ] where [ x ] is the largest integer less than or equal to x.

2.  Show that b_{n+1} = (b_n)/2 + 3/2; use this (and geometric series) to write down b_n explicitly.

1.  Conjecture that u_n = (n-1) (n-3) (n-5)... and prove the formula via induction.