已知(1-2x)100=a0+a1x+a2x2+…+a100x100,求: (1)a1+a2+…+a100 (2)a0+a2+a4+…+a100 (3)a1+a3+a5+…+a99 (4)|a0|+|a1|+…+|a100|

问题描述:

已知(1-2x)100=a0+a1x+a2x2+…+a100x100,求:
(1)a1+a2+…+a100
(2)a0+a2+a4+…+a100
(3)a1+a3+a5+…+a99
(4)|a0|+|a1|+…+|a100|

(1)∵已知(1-2x)100=a0+a1x+a2x2+…+a100x100,∴常数项a0=1.在所给的等式中,令x=1可得a0+a1+a2+a3+…+a100=1,∴a1+a2+a3+…+a100=0.(2)在所给的等式中,令x=1可得a0+a1+a2+a3+…+a100=1①,令x=-1可得得a...