=\(\frac{1}{2}.\frac{2}{3}...\frac{1998}{1999}.\frac{1999}{2000}\)= \(\frac{1}{2000}\)
Tính ra:
\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{199}{200}\)
Rút gọn:
\(\frac{1}{200}\)
Vậy đáp số là 1/200.
Chúc em hoc totos^^
\(\text{Ta thấy}\)\(1-\frac{1}{2}=\frac{1}{2};1-\frac{1}{3}=\frac{2}{3};...........1-\frac{1}{n}=\frac{n-1}{n}\)
\(\Rightarrow\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right)..........\left(1-\frac{1}{1999}\right)\left(1-\frac{1}{200}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}................\frac{1998}{1999}\)
\(=\frac{\text{(1.2.3.4....1998) }}{\text{(2.3.4.5...1999)}}=\frac{1}{1999}\)
\(ĐặtA=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).................\left(1-\frac{1}{1999}\right).\left(1-\frac{1}{2000}\right)\)
\(A=\frac{1}{2}.\frac{2}{3}.....\frac{1998}{1999}.\frac{1999}{2000}\)
\(A=\frac{1.2.3.4.5.....1999}{2.3.4.5.6.....2000}\)
\(=>A=\frac{1}{2000}\)
