\(A=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{11}-\frac{1}{14}\)
\(A=\frac{1}{2}-\frac{1}{14}\)
\(A=\frac{3}{7}\)
\(A=\)\(\frac{3}{5\times2}+\frac{3}{5\times8}+\frac{3}{8\times11}+...+\frac{3}{11\times14}\)
\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{11}-\frac{1}{14}\)
\(=\frac{1}{2}-\frac{1}{14}\)
\(=\frac{3}{7}\)
A = 3/5*2 + 3/5*8 + 3/8*11 + 3/11*14
A = 1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 + 1/11 - 1/14
A = 1/2 - 1/14
A = 6/14 = 3/7