Đáp án và lời giải
Đáp án:A
Lời giải:Ta có: $\begin{gathered} A = \frac{3}{4} \times \frac{8}{9} \times \frac{{15}}{{16}} \times \frac{{24}}{{25}} \times \frac{{35}}{{36}} \times \frac{{48}}{{49}} \times \frac{{63}}{{64}} \times \frac{{80}}{{81}} \times \frac{{99}}{{100}} \times \frac{{120}}{{121}} \ \\ \,\,\,\,\, = \frac{{1 \times 3}}{{2 \times 2}} \times \frac{{2 \times 4}}{{3 \times 3}} \times \frac{{3 \times 5}}{{4 \times 4}} \times \frac{{4 \times 6}}{{5 \times 5}} \times \frac{{5 \times 7}}{{6 \times 6}} \times \frac{{6 \times 8}}{{7 \times 7}} \times \frac{{7 \times 9}}{{8 \times 8}} \ \\ \,\,\,\,\,\,\,\,\, \times \frac{{8 \times 10}}{{9 \times 9}} \times \frac{{9 \times 11}}{{10 \times 10}} \times \frac{{10 \times 12}}{{11 \times 11}} \ \\ \,\,\,\,\, = \frac{{\left( {1 \times 2 \times 3 \times ... \times 10} \right) \times \left( {3 \times 4 \times 5 \times ... \times 12} \right)}}{{\left( {2 \times 3 \times 4 \times ... \times 11} \right) \times \left( {2 \times 3 \times 4 \times ... \times 11} \right)}} \ \\ \,\,\,\, = \frac{{1 \times 12}}{{11 \times 2}} = \frac{6}{{11}} \ \\ \end{gathered} $ Vậy $A = \frac{6}{{11}}.$
