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

Expansion of (47x)^(-(2)/(5)) is valid if

Show that the expansion of (x^(2)+(1)/(x))^(1) does not contain any term involving x^(-1)

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

Find the possible set of values of x for which expansion of (3-2x)^(1//2) is valid in ascending powers of x.

The range of x for which the expansion of (4+5x)^(-7//2) is valid

Find the interval of x, for which the expansion of (8 – 3x)^(3/2) in terms of power of x is valid.

Find the coefficient of : (i) x^3 in the expansion of (1 - x)^(-1/4) (ii) x^2 in the expansion of (5 - 3x)^(-1/3)