Question

已知在(1/2x^2-1/根号x)^n的展开式中,第9项为常数项求 n的值,展开式中x^5的系数,

Answer 1

C(n,8)(x^2/2)^(n-8)(-x^(-1/2))^8=C(n,8)(1/2)^(n-8)x^(2n-16-4),

2n-20=0,

n=10

-------------------

C(10,k)(-1)^k(1/2)^(10-k)x^(20-2k-k/2)

20-2k-k/2=5

k=6

C(10,5)/16

-------------------

6