In the expansion of (1 + x)^n, the coefficient of x^5 is the arithmetic mean of the coefficients of x^4 and x^6. Find the possible values of n.
Apart from the calculations, could you explain what is 'arithmetic mean'?
Binomial theorem~ 1 question
2010-08-31 8:20 am
回答 (1)
2010-08-31 9:02 am
✔ 最佳答案
arithmetic mean of a and b is (a+b)/22C(n,5)=C(n,4)+C(n,6)
2*n!/[5!*(n-5)!]= n!/[4!*(n-4)!] + n!/[6!*(n-6)!]
Multipling 4!*(n-6)!/n!, then
2/[5* (n-5)] = 1/[(n-4)(n-5)] + 1/30
Multipling 30(n-4)(n-5), then
12(n-4)=30+(n-4)(n-5), then n^2-21n+98=0
(n-7)(n-14)=0, n=7 or 14
Ans: n=7 or 14
收錄日期: 2021-04-13 17:29:31
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https://hk.answers.yahoo.com/question/index?qid=20100831000051KK00033