On the coefficients of the fourth term in (x-1) nth power expansion Calculate with the following formula Tr+1=C（n,r）a^（n-r）b^r If the coefficients of the second and fifth terms in the (x-1) nth power expansion are known to be equal, then the coefficients of the fourth term are equal

The fourth term, r = 3
T4=C(n,3)x^(n-3)(-1)^3
=-C(n,3)x^(n-3)

(x to the second power + 1 / x) n expansion, the fifth term is a constant term, (1) find n, (2) find the coefficient of the term containing x to the third power

The general term of (X & # 178; + 1 / x) ^ n is (X & # 178;) ^ (n-k) * x ^ (- K) * C (n, K) = x ^ (2n-3k) * C (n, K)
1) The fifth term is a constant term, k = 4, 2n-3k = 0, and the solution is n = 6
2) When 2n-3k = 3, k = 3, the coefficient is C (6,3) = 20

In the n-th power expansion of (a + 1 / a), the ratio of the coefficient of the fourth term to the coefficient of the fifth term is 1:2, and the exponent n and the term (n-3) are obtained

According to the binomial theorem: when n = 1, the coefficients are 1,1; when n = 2, the coefficients are 1,2,1; when n = 3, the coefficients are 1,3,3,1; when n = 4, the coefficients are 1,4,6,4,1; when n = 5, the coefficients are 1,5,10,10,5,1; when n = 6, the coefficients are 1,6,15,20,15,6,1; when n = 7, the coefficients are 1,7,21,35,35,21,7,1; when n = 8, the coefficients are 1,8,28,56,70,56,28,8,1; when n = 9, The coefficients are 1, 9, 36, 84, 126, 126, 84, 36, 9, 1; when n = 10, the coefficients are 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1; when n = 11, the coefficients are 1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1 It can be seen that n = 11 is the solution
The coefficient of (n-3) = 8 is 330, which should be 330 (a ^ 4 × (1 / a) ^ 7) = 330 / A ^ 3

On the coefficients of the fourth term in (x-1) nth power expansion Calculate with the following formula Tr+1=C（n,r）a^（n-r）b^r If the coefficients of the second and fifth terms in the (x-1) nth power expansion are known to be equal, then the coefficients of the fourth term are equal