Question

(1-1/10):(1+1/10):(1+1/11):(1+1/12): ... :(1+1/500)

Answer 1

\(\left(1-\dfrac{1}{10}\right):\left(1+\dfrac{1}{10}\right):\left(1+\dfrac{1}{11}\right):\left(1+\dfrac{1}{12}\right):...:\left(1+\dfrac{1}{500}\right)\)

=\(\dfrac{9}{10}:\dfrac{11}{10}:\dfrac{12}{11}:\dfrac{13}{12}:...:\dfrac{501}{500}\)

=\(\dfrac{9}{10}.\dfrac{10}{11}:\dfrac{12}{11}:\dfrac{13}{12}:...:\dfrac{501}{500}\)

=\(\dfrac{9}{11}:\dfrac{12}{11}:\dfrac{13}{12}:...:\dfrac{501}{500}\)=\(\dfrac{9}{501}\)=\(\dfrac{3}{167}\)