Question

Rút gọn
C = \(\left(1+\dfrac{1}{1.3}\right)\left(1+\dfrac{1}{2.4}\right)\left(1+\dfrac{1}{3.5}\right)...\left(1+\dfrac{1}{2014.2016}\right)\)

Answer 1

\(C=\left(1+\dfrac{1}{1.3}\right)\left(1+\dfrac{1}{2.4}\right)\left(1+\dfrac{3}{3.5}\right)...\left(1+\dfrac{2014}{2016}\right)\)

\(C=\dfrac{4}{1.3}.\dfrac{9}{2.4}.\dfrac{16}{3.5}.....\dfrac{4060225}{2014.2016}\)

\(C=\dfrac{2.2}{1.3}.\dfrac{3.3}{2.4}.\dfrac{4.4}{3.5}.....\dfrac{2015.2015}{2014.2016}\)

\(C=\dfrac{2.2.3.3.4.4.....2015.2015}{1.3.2.4.3.5.....2014.2016}\)

\(C=\dfrac{2.\left(3.2\right)\left(4.3\right).....\left(2015.2014\right).2015}{1.\left(3.2\right)\left(4.3\right).....\left(2015.2014\right).2016}\)\(\)

\(C=\dfrac{2.2015}{1.2016}\)

\(C=\dfrac{4030}{2016}\)\(=1\dfrac{2014}{2016}\).