HELP!!! F4 A maths 急!!10分

2006-11-01 2:51 am
試求(x^3 - 1/x )^24的展式中x^ -12 的係數pls
更新1:

請詳列步驟pls 聽日test喇,拜托

回答 (2)

2006-11-01 3:38 am
✔ 最佳答案
(x^3 - 1/x )^24
The (r+1)th term [第(r+1)項] = 24Cr (x^3)^(24-r) (x^ -1)^r
= 24Cr x^(72-4r)
For[對於] x^ -12 o個項, 72-4r = -12
r = 21
So, [所以,] coefficient of x^ -12 [x^ -12 ge係數]
= 24C21
=2024
參考: 對Binomial ge認識, 本人F.6 ,考完CE A.maths
2006-11-01 3:00 am
(x^3-1/x)^2
=(x^3)^2-2(x^3)(1/x)+(1/x)^2
=x^6-2x^2+1/x^2
=x^6-2x^2+x^(-2)
Because there is no term as x^(-12)
Therefore the coefficient is 0 or none

If you refer x^(-2)
The coefficient is 1


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