1a.) If (1+ x- 4x^2)^8 = 1 + ax + bx^2 + ..., find the values of a and b.
1b.)By considering the binomial expansion of (1 + x)^n and putting a suitable value of x, show that 1C0 + nC1 + nC2 + ... + nC(n-1) + nCn = 2^n,
where n is a natural number.
(請列式作答)
A.Maths Binomial
2009-09-02 3:04 am
回答 (1)
2009-09-02 3:18 am
✔ 最佳答案
1.a. (1 + x - 4x2)8= [1 + x(1 - 4x)]8
= 1 + 8C1(1)[x(1 - 4x)] + 8C2(1)[x(1 - 4x)]2 + ...
= 1 + 8x - 32x2 + 28x2 + ...
= 1 + 8x - 4x2 + ...
Comparing coefficients, a = 8, b = -4
b. (1 + x)n
= nC0 + nC1x + nC2x2 + ... + nC(n - 1)xn-1 + nCnxn
Put x = 1,
2n = nC0 + nC1 + nC2 + ... + nC(n - 1) + nCn
參考: Physics king
收錄日期: 2021-04-19 15:17:19
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