`(1)/(4)" " (1)/(2) " "(3)/(4)" "1" "1(1)/(4)" "1(1)/(2)" "1(3)/(4) ?`

(3)/(4)" of "((1)/(3)+(1)/(2))-:((1)/(7)+1(1)/(14))" of "2times(1)/(4)-(1)/(2)" of "(3)/(4)

The sum of the infinite series (1)/(2) ((1)/(3) + (1)/(4)) - (1)/(4)((1)/(3^(2)) + (1)/(4^(2))) + (1)/(6) ((1)/(3^(3)) + (1)/(4^(3))) - ...is equal to

[ 1 (1)/(4) div 1 (1)/(2) ] + [ 2 (1)/(3) xx 1 (3)/(4) ]=

Simplify : 8 (1)/(2)-[3 (1)/(4)-:{1(1)/(4) - (1)/(2) ( 1 (1)/(2)-(1)/(3)-(1)/(6))}]