數學問題一問...(thx)萬分感激!!!

1)the general term of (2+3x)^n : nCr(2^(n-r))(3^r)(x^r)
put r=3,x^3的系數=(nC3)(2^(n-3))(3^3)=[9n(n-1)(n-2)/2](2^(n-3))
put r=4,x^4的系數=(nC4)(2^(n-4))(3^4)=[27n(n-1)(n-2)(n-3)/8](2^(n-4))
{[9n(n-1)(n-2)/2](2^(n-3))}/{[27n(n-1)(n-2)(n-3)/8](2^(n-4))}=8/15
[n(n-1)(n-2)]/[n(n-1)(n-2)(n-3)]=1/5
5n(n-1)(n-2)=n(n-1)(n-2)(n-3)
n(n-1)(n-2)(n-8)=0
n=0(rejected),1(rejected),2(rejected),8
n=8

2)the general term of(x^2 - 1/2x)^9 :9Cr(x^2(9-r))((-1/2)^r)(x^r)
=9Cr((-1/2)^r)x^(18-r)
when 18-r=9 , r=9
x^9 項的系數=9C9((-1/2)^9)=-1/512

3)the general term of(x-1)(x+1)^8:8Cr(x^r)(x-1)

x^5 項的系數=8C4-8C5=14

4)(1+2x)^5 (1-x)^7=(1+10x+40x^2+...)(1-7x+21x^2+...)
x^2 的項:(21-70+40)x^2=-9x^2
5)(1+2x)^5=1+10x+40x^2+80x^3+80x^4+32x^5
(1.02)^5 =1+10(0.01)+40(0.01)^2+80(0.01)^3+80(0.01)^4+32(0.01)^5
=1+0.1+0.004+0.00008+0.0000008+0.0000000032
=1.104