Question

Tính tích

(1-1/2).(1-1/3).(1-1/4)..............(1-1/999).(1-1000)

Answer 1

\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{999}\right).\left(1-\frac{1}{1000}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{998}{999}.\frac{999}{1000}\)

\(=\frac{1.2.3.....998.999}{2.3.4.....999.1000}\)

\(=\frac{1}{1000}\)

Answer 2

\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{999}\right)\left(1-\frac{1}{1000}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{998}{999}.\frac{999}{1000}\)

\(=\frac{1}{1000}\)

p/s: chúc bạn học tốt

Answer 3

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

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

\(\Rightarrow\)BỎ CÁC SỐ: 2;3;4;...;99

\(=\frac{1}{1000}\)

Answer 4

Đáp án là : \(\frac{1}{1000}\)

Tk nha !!

Answer 5

( 1 - 1/2 ) . ( 1 - 1/3 ) . ( 1 - 1/4 ) . ... . ( 1 - 1/999 ) . ( 1 - 1/1000)

= 1/2 . 2/3 . 3/4 . ... . 998/999 . 999/1000

= 1 . 2 . 3 . ... . 998 . 999 / 2 . 3 . 4 . ... . 999 . 1000

= 1/1000