Question

A=3/5.10=3/10.15+.....+3/95.100

Answer 1

\(A=\dfrac{3}{5\cdot10}+\dfrac{3}{10\cdot15}+...+\dfrac{3}{95\cdot100}\)

\(=\dfrac{3}{5}\left(\dfrac{5}{5\cdot10}+\dfrac{5}{10\cdot15}+...+\dfrac{5}{95\cdot100}\right)\)

\(=\dfrac{3}{5}\left(\dfrac{1}{5}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{15}+...+\dfrac{1}{95}-\dfrac{1}{100}\right)\)

\(=\dfrac{3}{5}\left(\dfrac{1}{5}-\dfrac{1}{100}\right)\)\(=\dfrac{3}{5}\cdot\dfrac{19}{100}=\dfrac{57}{500}\)

Answer 2

\(A=\dfrac{3}{5.10}+\dfrac{3}{10.15}+.....+\dfrac{3}{95.100}\)

\(A=\dfrac{3}{5}\left(\dfrac{1}{5}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{15}+.....+\dfrac{1}{95}-\dfrac{1}{100}\right)\)

\(A=\dfrac{3}{5}\left(\dfrac{1}{5}-\dfrac{1}{100}\right)\)

\(=\dfrac{3}{5}.\dfrac{19}{100}=\dfrac{19}{500}\)