`(1+2x+x^(2))^(3)`

The solution of the inequation (1-2 x-3 x^(2))/(3 x-x^(2)-5) gt 0 is

If |x| lt 1 , then the coefficient of x^(5) in the expansion of (1+ 2x + 3x^(2) + ..........)^((-3)/2) is

The coefficient of x^5in(1+2x+3x^2+)^(-3//2)i s(|x|<1)

2 tan ^(-1) ""(2x)/(1-x^(2))=(pi)/(3)

Factorise (1-2x-x^(2))(1-2x+3x^(2))+4x^(4)

int(1+x+(x^(2))/(2!)+(x^(3))/(3!)+)dx

The sum of the series (1)/(1!)x+(2)/(2!)x^(2)+(3)/(3!)x^(3) ….. To infty is

Let l,m,n are the coefficients of x^5 in (1+2x+3x^2+…..)^(-3//2), (1+x+x^2 +x^3+….)^2, (1+x)^5 Respectively then :

lim_(x rarr 1)[1+(1+x)/(2!)+(1+x+x^2)/(3!)+...+oo] is equal to