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