In the expansion of (1+ax)^n, in ascending powers of x, the coefficient of x is 12....?

2010-11-06 11:49 am
In the expansion of (1+ax)^n, in ascending powers of x, the coefficient of x is 12 and the coefficient of x^3 is six times the coefficient of x^2, find a and n

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回答 (1)

2010-11-06 12:31 pm
✔ 最佳答案
1+ nax + n(n-1)/2 (ax)^2 + n(n-1)(n-2)/6 (ax)^3+ .....

from this we get
the coefficient of x is 12
na = 12 ----------------------------1

coefficient of x^3 = n(n-1)(n-2)/6 (a)^3 ----------------------2

coefficient of x^2 = n(n-1)/2 (a)^2 ----------------------------3

(2) is 6 times (3)

n(n-1)(n-2)/6 (a)^3 =6* n(n-1)/2 (a)^2

(n-2)a =18
na -2a =18

12 -2a = 18

a = -3 n = -4


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