Question

\(\dfrac{9}{20}\)-\(\dfrac{11}{30}\)+\(\dfrac{13}{42}\)+...+\(\dfrac{197}{9702}\)-\(\dfrac{199}{9900}\)

 

Answer 1

\(=\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{7}-...+\dfrac{1}{98}+\dfrac{1}{99}-\dfrac{1}{99}-\dfrac{1}{100}\)

=1/4-1/100

=25/100-1/100

=24/100=6/25