數學M1 既問題 - Ans.fyi 參考答案

數學M1 既問題

2011-06-19 6:19 am

我唔識用binomial therem二項式定理,
書係英文,我睇唔明,
可以簡單教我概念/公式嗎?

仲有呢題..
9C3 (3x)^9-r (-1除x^2)^r
點變
9C3 (-1)^r (3^{9-3}) (x^{9-3r])

9C3=C 9係C右邊既上面,3係C右邊既下面

同埋
find the coffefficient of x^3 in the expansion of (5+2X)^6
find the constant term in the expansin of (3x-1除x2)^9

呢兩題點計?(最重要步驟!!)

上面可能好難睇得明..
不過都唔該教下我..thx大大

回答 (1)

Tak Kin

2011-06-20 7:01 am

✔ 最佳答案

9C3 (3x)^9-r (-1除x^2)^rrewrite 9C3(3x)^9-r (-x^-2)^r= 9C3 [3^9-r] [x^9-r] [(-1)^r] [x^-2r]= 9C3 [(-1)^r] [3^9-r][x^9-3r] find the coffefficient of x^3 in the expansion of (5+2X)^6the (r+1)th term = 6Cr 5^6-r (2X)^r = 6Cr 5^6-r 2^r X^r for x^3 term = 6C3 5^6-3 2^3 X^3∴ the coffefficient of x^3 = 6C3 5^3 2^3 = 20000 find the constant term in the expansin of (3x-1除x2)^9the (r+1)th term = 9Cr (3x)^9-r (-x^-2)^r = 9Cr [(-1)^r] 3^9-r x^9-3rfor constant term : 9-3r = 0 ∴ r = 3and the constant term = 9C3(-1)^3 3^6 = -61236

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