更新1:
Find , in the expansion of [(1+1/x)^2] (2-x)^7,the coefficient of x
f.4 binomial
回答 (2)
2006-11-25 7:22 am
✔ 最佳答案
[(1+1/x)^2] (2-x)^7= (1 + 2/x + 1/x^2)[2^7 + 7(-x)(2)^6 + 21[(-x)^2](2)^5 + 35 [(-x)^3](2)^4 + ...]
= (1 + 2/x + 1/x^2)(128 - 448x + 672x^2 - 560x^3 + ...]
Therefore, coefficient of x
= (1)(-448) + (2)(672) + 1(-560)
= 336
2006-11-24 6:25 am
(1+1/x)^2 = 1 + 2(1/x) + (1/x)^2
(2-x)^7 = 2^7 + (7)(2^6)(-x) + (21)(2^5)(-x)^2 + ......
coefficient of the binomial
= (1)(2^7) + (7)(2^6)(-1)(2) + (21)(2^5)(1)
= -96
(2-x)^7 = 2^7 + (7)(2^6)(-x) + (21)(2^5)(-x)^2 + ......
coefficient of the binomial
= (1)(2^7) + (7)(2^6)(-1)(2) + (21)(2^5)(1)
= -96
參考: A maths textbook
收錄日期: 2021-04-30 22:20:50
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