Question

Answer 1

\(A=\dfrac{1}{2.3}+\dfrac{2}{3.5}+\dfrac{3}{5.8}+\dfrac{4}{8.12}+\dfrac{5}{12.17}+\dfrac{6}{17.23}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{23}\)

\(=\dfrac{1}{2}-\dfrac{1}{23}=\dfrac{21}{46}\)

Answer 2

\(A=\dfrac{1}{2.3}+\dfrac{2}{3.5}+\dfrac{3}{5.8}+\dfrac{4}{8.12}+\dfrac{5}{12.17}+\dfrac{6}{12.17}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{17}=\dfrac{1}{2}-\dfrac{1}{17}=\dfrac{15}{34}\)