For an=1.5an−1a_n = 1.5 a_{n-1}an=1.5an−1 with a0=1a_0 = 1a0=1 and bn=bn−1+nb_n = b_{n-1} + nbn=bn−1+n with b0=1b_0 = 1b0=1, which is true for sufficiently large nnn?
ana_nan grows exponentially while bnb_nbn grows polynomially; thus an>bna_n > b_nan>bn eventually
Both grow exponentially at the same rate
bnb_nbn grows faster because nnn is added at each step
Their growth rates are equivalent asymptotically