Tính giá trị của biểu thức ( tính nhanh nếu có thể)
Câu 17:
( \(1+\frac{1}{2}\) ) . ( \(1+\frac{1}{3}\) ) . ( \(1+\frac{1}{4}\) ) . ..... ( \(1+\frac{1}{2006}\) ) . ( \(1+\frac{1}{2007}\) )
Câu 18:
( \(1-\frac{1}{2}\) ) . ( \(1-\frac{1}{3}\) ) . ( \(1-\frac{1}{4}\) ) . ..... (\(1-\frac{1}{2006}\) ) . ( \(1-\frac{1}{2007}\)
Câu 19:
( \(2-\frac{3}{2}\) ) . ( \(2-\frac{4}{3}\) ) . ( \(2-\frac{5}{4}\) ) . ( \(2-\frac{5}{6}\) ) . ...... ( \(2-\frac{10}{9}\) )
Câu 20:
\(\text{( 1 - 1/4 ) . ( 1 - 1/9 ) . ( 1 - 1/16 ) . ..... ( 1 - 1/100 ) . ( 1 - 1 / 121)}\)
Câu 17:
\(\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{2006}\right).\left(1+\frac{1}{2007}\right)\)
=\(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{2007}{2006}.\frac{2008}{2007}\)
\(=\frac{2008}{2}=1004\)
Câu 18:
\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2006}\right).\left(1-\frac{1}{2007}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2005}{2006}.\frac{2006}{2007}\)
\(=\frac{1}{2007}\)
