The value of `(cos"" (pi)/(2)+isin ""(pi)/(2))(cos ((pi)/(2^2))+isin((pi)/(2^2))) (cos ((pi)/(2^3))+isin((pi)/(2^3)))"`
`………."oo` is

Explanation

`(cos.(pi)/(2)+ i sin.(pi)/(2))(cos.(pi)/(2^(2))+i sin.(pi)/(2^(2))) ...."to" oo`
`=cos((pi)/(2)+(pi)/(2^(2)) +....)+ isin ((pi)/(2)+(pi)/(2^(2))+.....)`
`=cos [(pi)/(2)(1+(1)/(2)+(1)/(2^(2))+.....)]+ isin[(pi)/(2)(1+(1)/(2)+(1)/(2^(2))+......)]`
`cos[(pi)/(2)((1)/(1-(1)/(2)))] + isin [(pi)/(2)((1)/(1-(1)/(2)))] = cos pi + isin pi =-1`