Question

A=1/_2x3 + 1/_3x4 + 1/_4x5 + 1/_5x6 + 1/_6x7 + 1/_7x8

Answer 1

\(A=\frac{3-2}{2\times3}+\frac{4-3}{4\times3}+\frac{5-4}{5\times4}+\frac{6-5}{6\times5}+\frac{7-6}{7\times6}+\frac{8-7}{8\times7}\)

\(A=\frac{3}{2\times3}-\frac{2}{2\times3}+\frac{4}{4\times3}-\frac{3}{4\times3}+\frac{5}{5\times4}-\frac{4}{5\times4}+\frac{6}{6\times5}-\frac{5}{6\times5}+\frac{7}{7\times6}\)\(-\frac{6}{7\times6}+\frac{8}{7\times8}-\frac{7}{7\times8}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)

\(=\frac{1}{2}-\frac{1}{8}=\frac{4}{8}-\frac{1}{8}=\frac{3}{8}\)