in yhe expansion of (1+3x)^2 * (1+x)^n
where n is positive integer the cofficient of x is 10
1.find the value of n
2.find the coefficient of x^2
f.4 amath question
2007-11-01 7:32 am
回答 (2)
2007-11-01 7:44 am
✔ 最佳答案
(1 + 3x)^2 = 1 + 6x + 9x^2(1 + x)^n = 1 + n * x + nC2 * x^2 + nC3 * x^3 + ... + n * x^(n-1) + x^n
1.
Coefficient of x = 1(n) + 6(1) = n + 6
n + 6 = 10, n = 4
2.
Coefficient of x^2
= 1(nC2) + 6(n) + 9(1)
= n! / [(n-2)! * 2!] + 6n + 9
= n(n-1) / 2 + 6n + 9
= 4(3) / 2 + 6(4) + 9
= 39
2007-11-01 8:10 am
4x2^3n
收錄日期: 2021-04-13 14:16:58
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20071031000051KK04646