Binomial

👨🏻‍🏫 學術台數學

知識就是力量

2010-04-27 4:12 am

As follows:

圖片參考：http://img441.imageshack.us/img441/227/screenhunter08apr262011.png

更新1:

Sorry your part b solution is wrong. By the way, there is a beautiful solution in part b without directly evaluating a1,a2,a3,...a8.

更新2:

I mean your ans.*

回答 (3)

lo824

2010-04-28 11:14 pm

✔ 最佳答案

(a) In the expansion of (5-3x)^8 in ascending powers of x,

The (r+1) th term
= 8Cr(5)^(8-r)(-3)^r x^r

Therefore,

a2
= 8C2(5)^6(-3)^2
= 3937500
a4
= 8C4(5)^4(-3)^4
= 3543750
a2 : a4 = 10 : 9
(b)

Let f(x)
= (5-3x)^8
= a1x^1 + a2x^2 + ... + a8x^8 + 5^8

By putting x = 1

f(1) = (5-3)^8 = a1 + a2 + .. + a8 + 5^8

Therefore, a1 + a2 + ... + a8 = 2^8 - 5 ^8
= -390369

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知識就是力量

2010-04-27 9:23 pm

nah, you got right steps
tips: Consider remainder theorem

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匿名

2010-04-27 4:59 am

Sorry that actually I don't know the solution, that's why i use such silly solution, Sorry

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