If `(x-4) / (x^2 - 5x + 6)` can be expanded in the ascending powers of x, then the coefficient of `x^3`

Expand in ascending powers of sin x,

Expand in ascending powers of x. 2^x ,

Expand in ascending powers of x. cos x,

Expand 1/(5+x) in ascending powers of x.

If (7x-1)/(1-5x+6x^(2)) is expanded in ascending powers of x when |x|<(1)/(3), then the cofficient of x^(n) is -A.2^(n)+4.3^(n), then A=

Expand (1)/(5+x) in ascending powers of x .

The coefficient of the (r +1)th term of (x +(1)/(x))^(20) , when expanded in the descending power of x , is equal to the coefficient of the 6th term of (x^(2) + 2 + (1)/(x^(2))) when expanded in ascending power of x . The value of r is

If (2+(x)/(3))^(55) is expanded in the ascending powers of x and the coefficients of powers of x in two consecutive terms of the expansion are equal then these terms of the expansion are 27,28 (D) 28,29

Consider the determinant D= |(x+2,2x+3,3x+4), (x+1, x+1, x+1), (0, 1, 3x +8)| If the determinant is expanded in the power of x, the coefficient of x is