A = \(\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}....\dfrac{899}{900}\)
= \(\left(\dfrac{1.3}{2.2}\right).\left(\dfrac{2.4}{3.3}\right).\left(\dfrac{3.5}{4.4}\right)...\left(\dfrac{29.31}{30.30}\right)\)
= \(\left[\left(1.2.3...29\right).\left(3.4.5...31\right)\right]:\left[\left(2.3.4...30\right).\left(2.3.4...30\right)\right]\)
= \(\dfrac{1.2.3...29}{2.3.4...30}.\dfrac{3.4.5...31}{2.3.4...30}\)
= \(\dfrac{1}{30}.\dfrac{31}{2}\)
= \(\dfrac{31}{62}\)
A= \(\dfrac{3}{4}\).\(\dfrac{8}{9}\).\(\dfrac{15}{16}\).....\(\dfrac{899}{900}\)
A= \(\dfrac{1.3}{2.2}\).\(\dfrac{2.4}{3.3}\).\(\dfrac{3.5}{4.4}\).....\(\dfrac{29.31}{30.30}\)
A= \(\dfrac{\left(1.2.3....29\right)}{\left(2.3.4....30\right)}\) . \(\dfrac{\left(3.4.5....31\right)}{\left(2.3.4....30\right)}\)
A= \(\dfrac{1.2.3....29}{2.3.4....30}\) . \(\dfrac{3.4.5...31}{2.3.4...30}\)
A= \(\dfrac{1}{30}\) . \(\dfrac{31}{2}\)
A= \(\dfrac{31}{6}\)
