What is the value of 7/2 + 113 + 7/6 + 1115 + 712 + 1135 + ........ + 7156 + 11575

Answer: Option D

$$\begin{array}{rl}& \frac{7}{2}+\frac{11}{3}+\frac{7}{6}+\frac{11}{15}+\frac{7}{12}+\frac{11}{35}+........+\frac{7}{156}+\frac{11}{575}\\ & =\left(\frac{7}{2}+\frac{7}{6}+\frac{7}{12}+........+\frac{7}{156}\right)+\left(\frac{11}{3}+\frac{11}{15}+\frac{11}{35}+........+\frac{11}{575}\right)\\ & =7\left(\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+........+\frac{1}{12\times 13}\right)+\frac{11}{2}\left(\frac{2}{1\times 3}+\frac{2}{3\times 5}+\frac{2}{5\times 7}+........+\frac{1}{23\times 25}\right)\\ & =7\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+........+\frac{1}{12}-\frac{1}{13}\right)+\frac{11}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+........+\frac{1}{23}-\frac{1}{25}\right)\\ & =7\left(1-\frac{1}{13}\right)+\frac{11}{2}\left(1-\frac{1}{25}\right)\\ & =\frac{7\times 12}{13}+\frac{11\times 24}{2\times 25}\\ & =\frac{84}{13}+\frac{132}{25}\\ & =\frac{2100+1716}{325}\\ & =\frac{3816}{325}\end{array}$$