find the greatest term in the expansion of (1+x) raised to thepower of10, x=2/3
Hmmm. seems like a pointless waste of time. Any exercise to see whether you understand Pascal's Triangle could involve much less work.
Anyway, the coefficients of (1+x)^10 are
1 10 45 120 210 252 210 120 45 10 1
The trailing terms get less and less when x<1, so we just have to look at the first 6 terms:
1 10*2/3 45*4/9 120*8/27 210*16/81 252*32/243
1 6.66 20 35.55 41.48 33.18
we have a winner: 210*16/81