If the coefficient of x^2 in (1-2x+x^2)^n is 66
Find value of n and coefficient of x^3
Thank you!
Binomial plzzzzz?
2016-03-30 4:32 pm
回答 (3)
2016-03-30 4:40 pm
✔ 最佳答案
Hint: (1-2x+x²)ⁿ = ((x-1)²)ⁿ = (x-1)²ⁿLook at Pascal's triangle. The only entries equal to 66 are in the expansion of (a+b)¹², so n = 6
:::::
x² is the 11th term in the expansion of (x-1)¹², so x³ is the 10th term in the expansion.
coefficient of x³ = 12!/(9!3!) = 10·11·12/(2·3) = 220
2016-03-30 4:41 pm
6 and -220
2016-03-30 4:35 pm
Do your own homework!
收錄日期: 2021-04-23 23:45:31
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