The expansion of `1/(4 - 3x)^(1/2)` by binomial theowill be valid, if

Binomial expansion of (x+1)^(6)

For beta ne 0 , if the coefficient of x^(3) in the binomial expansion of (1 + betax)^(6) and the coefficient of x^(4) in the binomial expansion of (1 - betax)^(8) are equal, then the value of beta is

Expansion of (5)/(2-x)+(1)/(1+3x) is valid if

Show that the expansion of (1+x)^(1/2) is not valid when x=3.

The expansion of (3x+2)^(-1/2) is valid in ascending powers of x if x lies in the interval.

(ii) Find the coefficient of x^(n) in the expansion of (x)/((x-1)^(2)(x-2)) in which the expansion is valid.

The expansion of (3x+2)^(-(1)/(2)) is valid in ascending powers of x, if x lies in the interval.