If `x` is positive, the sum to infinity of the series `1/(1+x)-(1-x)/((1+x)^2)+(1-x) ^2/((1+x)^3)-(1-x)^3/((1+x)^4)+ i s` 1/2 (b) 3/4 (c) 1 (d) none of these

Explanation

Given,

`1/(1+x)-(1-x)/((1+x)^2)+(1-x)
^2/((1+x)^3)-(1-x)^3/((1+x)^4)+...oo`

Here `a=1/(1+x)` and `r=-(1-x)/(1+-x)`


so,sum of infinite terms is
`S=a/(1-r)`

`s=(1/(1+x))/(1-(-(1-x)/(1+-x)))`

`s=(1/(1+x))/((1+x+1-x)/(1+x))`

...