Question

\(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+...\dfrac{1}{90}\)

Answer 1

\(\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{90}\)

\(=\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{9\cdot10}\)

\(=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}\)

\(=\dfrac{1}{3}-\dfrac{1}{10}=\dfrac{7}{30}\)

Answer 2

   \(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+....\dfrac{1}{90}\)
= \(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+....+\dfrac{1}{9.10}\)|
= \(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+....+\dfrac{1}{9}-\dfrac{1}{10}\)
=\(\dfrac{1}{3}-\dfrac{1}{10}\)
=\(\dfrac{10}{30}-\dfrac{3}{30}\)
=\(\dfrac{7}{30}\)

Answer 3

=1/3.4+1/4.5+1/5.6+....+1/9.10

=1/3-1/4+1/4-1/5+1/5-1/6+.....+1/9-1/10

=1/3-1/10

=7/30