1.
It is given that n is a positive integer and constant term in expansion of (2+(x/2))^n is 64.
a.)Find the value of n.
b.)Find the 4th term of the expansion in ascending powers of x.
F.4math !binomial theorem!help
2010-08-27 3:23 pm
回答 (1)
2010-08-27 3:50 pm
✔ 最佳答案
For (a + b)^n, general term is nCr (a)^(n - r) (b)^r.Now a = 2, b = x/2, so general term is nCr (2)^(n - r) (x/2)^r = nCr (2)^(n - r) (x)^r (2)^(-r). = nCr (2)^(n - 2r) x^r.
For constant term, power of x is zero, that is r = 0
so nC0 (2^n) = 64, 2^n = 64, n = 6.
(b) The 4 th term is (6C3) (2^3) (x/2)^3 = 20x^3.
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