Question

A =1/4+ 1/12+ 1/24+ 1/40 + 1/60 + 1/84

Answer 1

A = 1/4 + ... +1/84

A = 2/8 + 2/24 + ... + 2/168

A = 2/2.4 + 2/4.6 + ... + 2/12.14

A = 1/2 - 1/4 + 1/4 - 1/6 + .. + 1/12 - 1/14

A = 1/2 - 1/14

A = 6/14 = 3/7

Answer 2

A = 2/8 + 2/24 + ... + 2/168

A = 2/2.4 + 2/4.6 + ... + 2/12.14

A = 1/2 - 1/4 + 1/4 - 1/6 + .. + 1/12 - 1/14

A = 1/2 - 1/14

A = 3/7

Answer 3

\(A=\frac{2}{8}+\frac{2}{24}+\frac{2}{48}+...+\frac{2}{168}\)

\(A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{12.14}\)

\(A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{12}-\frac{1}{14}\)

\(A=\frac{1}{2}-\frac{1}{14}\)

\(A=\frac{3}{7}\)