find the coefficient of x^10 in the expansion of (1-x)(1+2x)^40
Please help me and teach me~thanks
find the coefficient of. . .
2008-10-11 7:48 am
回答 (2)
2008-10-11 8:50 am
✔ 最佳答案
(1-x)(1+2x)^40= (1 - x)[1 + 40(2x) + ..... + 40C9(2x)^9 + 40C10(2x)^10 + .....]
= (1 - x)(1 + 80x + .....273438880(2^9)x^9 + 847660528(2)^10x^10 + ....)
So, the coefficent of x^10 = 1* 847660528(2)^10 - 273438880(2)^9
= 1695321056(2)^9 - 273438880(2)^9
= 1421882176(2)^9
= 7.280036741*(10)^11
參考: Myself
2008-10-11 5:48 pm
(1-x)(1+2x)^40=(1+2X)^40-x(1+2x)^40
=40Σr=0 40Cr(2x)^r- x40Σr=0 40Cr(2x)^(
∴the coefficient of x^10=40C10x2^10-40C9x2^9
=7.28x10^11
=40Σr=0 40Cr(2x)^r- x40Σr=0 40Cr(2x)^(
∴the coefficient of x^10=40C10x2^10-40C9x2^9
=7.28x10^11
收錄日期: 2021-04-13 16:13:04
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https://hk.answers.yahoo.com/question/index?qid=20081010000051KK02234