(1- 1/2 ) * ( 1-1/3 ) * ( 1 - 1/4 ) .... (1- 1/4 )=?

 

    (1-1/2)(1-1/3)...(1-1/100)

= 1/2 . 2/3 . 3/4 ....99/100

=\(\frac{1\cdot2\cdot3\cdot4\cdot...\cdot99}{2.3.4....100}=\frac{1}{100}\)

Ta có:

 \(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{100}\right)\)

\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{99}{100}\)

\(=\frac{1\times2\times3\times4\times...\times99}{2\times3\times4\times...\times100}\)

\(=\frac{1}{100}\)

Vậy:\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{100}\right)=\frac{1}{100}\)