The sum of the series $\large\frac{3}{4.8}-\frac{3.5}{4.8.12}+\frac{3.5.7}{4.8.12.16}-...........$

Question

\[\begin {array} {1 1} (a)\;\sqrt {\frac{3}{2}}-\frac{3}{4} & \quad (b)\;\sqrt {\frac{2}{3}}-\frac{3}{4} \\ (c)\;\sqrt {\frac{3}{2}}-\frac{1}{4} & \quad (d)\;\sqrt {\frac{2}{3}}-\frac{1}{4} \end {array}\]

Answer 1

$(b)\;\sqrt {\frac{2}{3}}-\frac{3}{4}$