Trả lời
A=(1-1/2)(1-1/4)(1-1/5).....(1-1/2018)(1-1/2019)
=1/2.3/4.4/5......2017/2018.2018/2019
=1/2.1/2019
=1/4038.
Nhưng theo mk nghĩ đề phải như thế này>
A=(1-1/3)(1-1/4)(1-1/5)........(1-2018)(1-2019)
=2/3.3/4.4/5......2017/2018.2018/2019
=2/2019.
\(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{2018}\right)\left(\frac{1}{2019}\right)\)
\(=\frac{1}{2}.\frac{3}{4}.\frac{4}{5}.....\frac{2017}{2018}.\frac{1}{2019}=\frac{1}{2}.\frac{3}{2018}.\frac{1}{2019}=\frac{1}{2716228}\)
Vậy\(A=\frac{1}{2716228}\)
Bài làm
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)....\left(1-\frac{1}{2018}\right)\left(1-\frac{1}{2019}\right)\)
\(=\frac{1}{2}.\frac{3}{4}.\frac{4}{5}...\frac{2017}{2018}.\frac{2018}{2019}\)
\(=\frac{3}{2}.\frac{1}{2019}\)
\(=\frac{3}{4038}\)
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