The expansion of `log.(1+x+x^(2))/(1-x+x^(2))` as ascending powers of x is

If x is very small and neglecting x^(3) and higher powers of x then the expansion of log(1+x^(2))-log(1+x)-log(1-x) as ascending powers of x is

If |x|lt1 then the coefficient of x^(3) in the expansion of log(1+x+x^(2)) is ascending power of x is

If |x|lt1 then the coefficient of x^(3) in the expansion of log(1+x+x^(2)) is ascending power of x is

In the expansion of (e^(x)-1-x)/(x^(2)) is ascending powers of x the fourth term is

In the expansion of (e^(x)-1-x)/(x^(2)) is ascending powers of x the fourth term is

If |x|lt1 , the coefficient of x^(3) in the expansion of log(1+x+x^(2)) in ascending power of x, is

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

The coefficient of x^(4) in the expansion of {sqrt(1+x^(2))-x}^(-1) in ascending powers of x when |x|<1, is 0 b.(1)/(2) c.-(1)/(2) d.-(1)/(8)

Find the coefficient of x in the expansion of [sqrt(1+x^(2))-x]^(-1) in ascending power of x when |x|<1