(a)find the value of n.
(b)find the constant term of the expansion.
點樣做?請寫出process...
更新1:
ascending,term,constant
中四既binonmial theorem題目
2009-10-10 7:38 am
when( 3x^5 + 1/x^2 )^n is expanded in ascejding powers of x, the 5th yerm of the expansion is a comstant.
(a)find the value of n.
(b)find the constant term of the expansion.
點樣做?請寫出process...
(a)find the value of n.
(b)find the constant term of the expansion.
點樣做?請寫出process...
回答 (2)
2009-10-10 8:03 am
✔ 最佳答案
(a) (3x^5 + 1/x^2 )^n
= (1/x^2 + 3x^5)^n
= ∑[k=0 to n]C(n,k) [(1/x^2)^(n-k)][(3x^5)^(k)]
The fifth term corresponds to k = 4
C(n,4)[(1/x^2)^(n-4)][(3x^5)^4]
The index of x is (-2)(n- 4) + (5)(4) = 0
20 - 2(n - 4) = 0
n = 14
(b) The constant term is C(14,4)3^4 = 81,081
2009-10-10 8:12 am
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