Question

a, Tìm x

x + ( x + \(\dfrac{1}{1.3}\)) + (x + \(\dfrac{1}{3.5}\)) +.........+ ( x + \(\dfrac{1}{19.21}\))=1

b, Rút gọn

A=\(\dfrac{3}{4}\) . \(\dfrac{8}{9}\) . \(\dfrac{15}{16}\) . \(\dfrac{24}{25}\) . ...... .\(\dfrac{99}{100}\)

Answer 1

\(A=\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}.\dfrac{24}{25}.....\dfrac{99}{100}\)

\(\Leftrightarrow A=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}.\dfrac{4.6}{5.5}.....\dfrac{9.11}{10.10}\)

\(=\dfrac{1.3.2.4.3.5.4.6....9.11}{2.2.3.3.4.4.5.5.....10.10}\)

\(=\dfrac{\left(1.2.3.4.5....9\right).\left(2.3.4.5.6.....11\right)}{\left(2.3.4.5.6.....10\right)\left(2.3.4.5.6.....10\right)}\)

\(=\dfrac{11}{10}\)