Question

1-\(\dfrac{1}{12}\)-\(\dfrac{1}{20}\)-\(\dfrac{1}{30}\)-...-\(\dfrac{1}{210}\)

Answer 1

1-​\(\dfrac{1}{12}\)-\(\dfrac{1}{20}\)-\(\dfrac{1}{30}\)-...-\(\dfrac{1}{210}\)

=1-(\(\dfrac{1}{12}\)+\(\dfrac{1}{20}\)+\(\dfrac{1}{30}\)+...+\(\dfrac{1}{210}\))

=1-(\(\dfrac{1}{3.4}\)+\(\dfrac{1}{4.5}\)+\(\dfrac{1}{5.6}\)+...+\(\dfrac{1}{14.15}\))

=1-(\(\dfrac{1}{3}\)-\(\dfrac{1}{4}\)+\(\dfrac{1}{4}\)-\(\dfrac{1}{5}\)+\(\dfrac{1}{5}\)-\(\dfrac{1}{6}\)+...+\(\dfrac{1}{14}\)-\(\dfrac{1}{15}\))

=1-(\(\dfrac{1}{3}\)-\(\dfrac{1}{15}\))

=1-\(\dfrac{4}{15}\)

=\(\dfrac{11}{15}\)