Question

A=1/1*3+1/3*5+1/5*7+...+1/19*21+1/21*23 = ?

Answer 1

\(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{19.21}+\frac{1}{21.23}\)

\(A=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{19.21}+\frac{2}{21.23}\right)\)

\(A=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}+\frac{1}{21}-\frac{1}{23}\right)\)

\(A=\frac{1}{2}\left(1-\frac{1}{23}\right)\)

\(A=\frac{1}{2}.\frac{22}{23}\)

\(A=\frac{11}{23}\)