若(2-x)^100=a0+a1x+a2x^2+……+a100x^100 求:(1) ao+a1+a2+……+a100的值 (2) a0(3) |a0|+|a1|+|a2|+……+|a100|的值(4)a0+a2+a4+……+a100的值(5)a1+a3+a5+……a99的值
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![若(2-x)^100=a0+a1x+a2x^2+……+a100x^100 求:(1) ao+a1+a2+……+a100的值 (2) a0(3) |a0|+|a1|+|a2|+……+|a100|的值(4)a0+a2+a4+……+a100的值(5)a1+a3+a5+……a99的值](/uploads/image/z/11556366-6-6.jpg?t=%E8%8B%A5%282-x%29%5E100%3Da0%2Ba1x%2Ba2x%5E2%2B%E2%80%A6%E2%80%A6%2Ba100x%5E100+%E6%B1%82%3A%281%29+ao%2Ba1%2Ba2%2B%E2%80%A6%E2%80%A6%2Ba100%E7%9A%84%E5%80%BC+%282%29+a0%EF%BC%883%EF%BC%89+%7Ca0%7C%2B%7Ca1%7C%2B%7Ca2%7C%2B%E2%80%A6%E2%80%A6%2B%7Ca100%7C%E7%9A%84%E5%80%BC%EF%BC%884%EF%BC%89a0%2Ba2%2Ba4%2B%E2%80%A6%E2%80%A6%2Ba100%E7%9A%84%E5%80%BC%EF%BC%885%EF%BC%89a1%2Ba3%2Ba5%2B%E2%80%A6%E2%80%A6a99%E7%9A%84%E5%80%BC)
若(2-x)^100=a0+a1x+a2x^2+……+a100x^100 求:(1) ao+a1+a2+……+a100的值 (2) a0(3) |a0|+|a1|+|a2|+……+|a100|的值(4)a0+a2+a4+……+a100的值(5)a1+a3+a5+……a99的值
若(2-x)^100=a0+a1x+a2x^2+……+a100x^100 求:
(1) ao+a1+a2+……+a100的值
(2) a0
(3) |a0|+|a1|+|a2|+……+|a100|的值
(4)a0+a2+a4+……+a100的值
(5)a1+a3+a5+……a99的值
若(2-x)^100=a0+a1x+a2x^2+……+a100x^100 求:(1) ao+a1+a2+……+a100的值 (2) a0(3) |a0|+|a1|+|a2|+……+|a100|的值(4)a0+a2+a4+……+a100的值(5)a1+a3+a5+……a99的值
1.
令x=1
a0+a1+a2+...+a100=(2-1)^100=1^100=1
2.
令x=0
a0=(2-0)^100=2^100
3.
x为负时,对于an,n为奇数时an0
令x=-1
a0-a1+a2-a3+...+a100=[2-(-1)]^100=3^100
|a0|+|a1|+|a2|+...+|a100|
=a0-a1+a2-a3+...+a100
=3^100
4.
a0-a1+a2-a3+...+a100 (1)
a0+a1+a2+...+a100=1 (2)
(1)+(2)
2(a0+a2+...+a100)=3^100 +1
a0+a2+...+a100=(3^100 +1)/2
5.
(2)-(1)
2(a1+a3+...+a99)=1-3^100
a1+a3+...+a99=(1-3^100)/2