For (a + b)^n = sum C(n,r)*a^{n-r}*b^r, the ratio of consecutive terms: |T_{r+1}/T_r| = |(n-r+1)/r| * |b/a|.

Set |T_{r+1}/T_r| >= 1: r <= (n+1)|b|/(|a|+|b|).

Let this bound be m. If m is integer, T_m and T_{m+1} are both numerically greatest. If m is not integer, T_{floor(m)+1} is the unique greatest term.

Example: Numerically greatest term of (2+3x)^9 when x = 1. |b/a| = 3/2. Bound: 103/5 = 6. Since m = 6 is integer, T_6 and T_7 are both greatest. T_7 = C(9,6)2^33^6 = 848*729 = 489888.