Evaluate `lim_(xto1)(sqrt(x)+sqrt(sqrt(x))+sqrt(sqrt(sqrtx))+sqrt(sqrt(sqrt(sqrt(x))))-4)/(x-1).`

Explanation

`underset(xto1)lim(sqrt(x)+sqrt(sqrt(x))+sqrt(sqrt(sqrtx))+sqrt(sqrt(sqrt(sqrt(x))))-4)/(x-1)`
`=underset(xto1)lim(x^(1//2)+x^(1//4)+x^(1//8)+x^(1//16)-4)/(x-1)`
`=underset(xto1)lim((x^(1//2)-1)/(x-1)+(x^(1//4)-1)/(x-1)+(x^(1//8)-1)/(x-1)+(x^(1//16)-1)/(x-1))`
`=1/2+1/4+1/8+1/16=(8+4+2+1)/(16)=15/16`