Question

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:

 \(\text{( 1 - 1/4 ) . ( 1 - 1/9 ) . ( 1 - 1/16 ) . ..... ( 1 - 1/100 ) . ( 1 - 1 / 121)}\)

 

Answer 1

Câu 17:

\(\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{2006}\right).\left(1+\frac{1}{2007}\right)\)

=\(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{2007}{2006}.\frac{2008}{2007}\)

\(=\frac{2008}{2}=1004\)

Answer 2

Câu 18:

\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2006}\right).\left(1-\frac{1}{2007}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2005}{2006}.\frac{2006}{2007}\)

\(=\frac{1}{2007}\)

Answer 3

Câu 19 hình như sai đề