1a) use the binomial series to expand (2- 3x) ^10 in ascending powers of x up to and including the term in x^3, giving each coefficient as an integer.
b) use your series expansion, with a suitable value for x, to obtain an estimate for 1.97^10 giving your answer to 2 d.p.
2) Expand (x- 1 over x) ^5, simplifying the coefficients.
Binomial
2009-05-25 5:12 am
回答 (1)
2009-05-25 9:05 pm
✔ 最佳答案
1.a. By Binomial Expansion,(2 - 3x)10
= (2)10 + 10C1(2)9(-3x) + 10C2(2)8(-3x)2 + 10C3(2)7(-3x)3 + ...
= 1024 - 15 360x + 103 680x2 - 414 720x3 + ...
b. (1.97)10
= [2 - 3(0.01)]10
= 1024 - 15 360(0.01) + 103 680(0.01)2 - 414 720(0.01)3 + ...
= 880.35 (2 d.p.)
2. (x - 1/x)5
= x5 + 5C1x4(-1/x) + 5C2x3(-1/x)2 + 5C3x2(-1/x)3 + 5C4x(-1/x)4 + (-1/x)5
= x5 - 5x3 + 10x - 10/x + 5/x3 - 1/x5
參考: Physics king
收錄日期: 2021-04-19 14:29:33
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