已知(1-2x)n=a0+a1x+a2x2+…+anxn,(n∈N*),且a2=60.(1)求n的值; (2)求-a12+a222-a323+…+(

2024-11-01 21:46:02
推荐回答(1个)
回答1:

(1)由题意可得 T3

C
(?2x)2=4?
n(n?1)
2
x2,故有 a2=2n(n-1)=60,解得n=6.
(2)由于Tr+1=
C
?(-2x)r=ar?xr,∴ar=(-2)r?
C
,∴(-1)r?
ar
2r
=
C

故-
a1
2
+
a2
22
-
a3
23
+…+(-1)n
an
2n
=
C
+
C
+
C
+…+
C
=26-1=63.