(Ⅰ)在(1+x)+(1+x)2+(1+x)3+…+(1+x)n=a0+a1x+a2x2+…+anxn中,
令x=0,可得a0=n,易得an=1.
再令x=1,可得2+22+23+…+2n=a0+a1+a2+a3+…+an-1 +an=n+1+a1+a2+a3+…+an-1 ,
∴a1+a2+a3+…+an-1=2+22+23+…+2n-n-1=
-n-1=2n+1-n-3.2(1?2n) 1?2
再根据2+22+23+…+2n=29-n,可得 2n+1-n-3=29-n,求得n=4.
(Ⅱ)由所给的等式可得 a3=
+
C
+
C
+…+
C
=
C
=
C
=(n+1)?n?(n?1)?(n?2) 4×3×2×1
(n+1)?n?(n?1)?(n?2) 24