" (i) "quad 1+2x+3x^(2)+4x^(3)+...

If f(x) = {{:( 1-2x +3x^(2) -4x^(3) +......infty,"for" xne 1),( 1,"for " x=-1):},then f(x) is

Sum up to n terms the series 1+ 2x + 3x^(2) + 4x^(3) + ...

If | x| lt 1, then the coefficient of x ^(n) in (1 + 2x + 3x ^(2)+ 4x ^(3) +...) ^(1//2), is :

The sum of series 1 + 2x + 3x^(2) + 4x^(3) + ...... up to infinity when x lies between 0 and 1 i.e., 0 lt x lt 1 is

The sum of the series 1 + 2x + 3x^(2) + 4x^(3) +"…." to oo where x lies between 0 and 1 i.e., 0 lt x lt 1 is :

int(1+2x+3x^(2)+4x^(3)+ . . .)dx=

Evaluate: int(1+2x+3x^(2)+4x^(3)+...)dx,quad (<|x|<1)

The coefficient of x^(10) in the expansion of (1-2x+3x^(2)-4x^(3)+...oo)^(2) is