Question

rút gọn biểu thức A= \(\frac{3}{4}\).\(\frac{8}{9}\).\(\frac{15}{16}\).\(\frac{24}{25}\).........\(\frac{899}{900}\) ta được a

Answer 1

\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}......\frac{889}{900}\)

\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{29\cdot31}{30.30}\)

\(=\frac{1.3.2.4.3.5.....29.31}{2.2.3.3.4.4....30.30}\)

\(=\frac{\left(1.2.3....29\right)\left(3.4.5...31\right)}{\left(2.3.4....30\right)\left(2.3.4.....30\right)}\)

\(=\frac{1.31}{30.2}=\frac{31}{60}\)