Question

Câu cuối cùng đè thi học kì của mình là

( \(1-\dfrac{1}{21}\)).(\(1-\dfrac{1}{28}\)).(\(1-\dfrac{1}{36}\))..........(\(1-\dfrac{1}{1326}\))

MONG CÁC BẠN MAU CHÓNG GIẢI GIÙM

Answer 1

Ta có:

\(\left(1-\dfrac{1}{21}\right)\left(1-\dfrac{1}{28}\right)\left(1-\dfrac{1}{36}\right)...\left(1-\dfrac{1}{1326}\right)\)

\(=\dfrac{20}{21}.\dfrac{27}{28}.\dfrac{35}{36}...\dfrac{1325}{1326}\)

\(=\dfrac{5.8:2}{6.7:2}.\dfrac{6.9:2}{7.8:2}.\dfrac{7.10:2}{8.9:2}...\dfrac{50.53:2}{51.52:2}\)

\(=\dfrac{5.8}{6.7}.\dfrac{6.9}{7.8}.\dfrac{7.10}{8.9}...\dfrac{50.53}{51.52}\)

\(=\dfrac{\left(5.6.7...50\right).\left(8.9.10...53\right)}{\left(6.7.8..51\right).\left(7.8.9...52\right)}\)

\(=\dfrac{5.53}{51.7}\)

\(=\dfrac{265}{357}\)