(2x-1/2)^6展開式通式為 C(6,n) [(2x)^n] [(-1/2)^(6-n)],n為0-6的整數(shù)
常數(shù)項(xiàng) 即 n=0,C(6,0) [(2x)^0] [(-1/2)^(6-0)] = (-1/2)^6 = 1/64
二項(xiàng)式,即n=2,C(6,2) [(2x)^2] [(-1/2)^(6-2)] = 15 * 4x^2 * 1/16 = 14x^2/4,
即二項(xiàng)式系數(shù)為15/4.
這類題目 一般形式為(ax+b)^k,a、b為常數(shù),
展開式通式即為C(k,n) [(ax)^n] [b^(k-n)],0≤n≤k,且n為整數(shù)
m項(xiàng)式即x的次數(shù)為m,即n=m,常數(shù)項(xiàng)的次數(shù)則為 k-m
如二項(xiàng)式,則n=2,常數(shù)項(xiàng)次數(shù)為 k-2