Question

Tính bằng cách hợp lí: (1-1/1007)*(1-1/1008)*(1-1/1009)*...*(1-1/1012)

Answer 1

\(\left(1-\frac{1}{1007}\right)\left(1-\frac{1}{1008}\right)\left(1-\frac{1}{1009}\right)\left(1-\frac{1}{1010}\right)\left(1-\frac{1}{1011}\right)\left(1-\frac{1}{1012}\right)\)

\(=\frac{1006}{1007}\cdot\frac{1007}{1008}\cdot\frac{1008}{1009}\cdot\frac{1009}{1010}\cdot\frac{1010}{1011}\cdot\frac{1011}{1012}\)

\(=\frac{1006\cdot1007\cdot1008\cdot1009\cdot1010\cdot1011}{1007\cdot1008\cdot1009\cdot1010\cdot1011\cdot1012}=\frac{503}{506}\)

Answer 2

=\(\frac{1006}{1007}.\frac{1007}{1008}.....\frac{1011}{1012}\)

=\(\frac{1006}{1012}\)

=\(\frac{503}{506}\)

nếu sai sót mong mọi người sửa lỗi đúng thì ủng hộ

Answer 3

\(\left(1-\frac{1}{1007}\right)\left(1-\frac{1}{1008}\right)\left(1-\frac{1}{1009}\right)...\left(1-\frac{1}{1012}\right)\)

\(=\frac{1006}{1007}\cdot\frac{1007}{1008}\cdot\frac{1008}{1009}\cdot...\cdot\frac{1011}{1012}\)

\(=\frac{1006\cdot1007\cdot1008\cdot...\cdot1011}{1007\cdot1008\cdot1009\cdot...\cdot1012}=\frac{1006}{1012}=\frac{503}{506}\)

Answer 4

\(\left(1-\frac{1}{1007}\right)\left(1-\frac{1}{1008}\right)\left(1-\frac{1}{1009}\right)...\left(1-\frac{1}{1012}\right)\)

\(=\frac{1006}{1007}.\frac{1007}{1008}.\frac{1008}{1009}....\frac{1011}{1012}\)

\(=\frac{1006.1007.1008....1011}{1007.1008.1009....1012}\)

\(=\frac{1006}{1012}=\frac{503}{506}\)

Answer 5

\((1-\frac{1}{1007}).(1-\frac{1}{1008}).(1-\frac{1}{1009})...(1-\frac{1}{1012})\)

\(=\frac{1006}{1007}.\frac{1007}{1008}.\frac{1008}{1009}...\frac{1011}{1012}\)

\(=\frac{1006.1007.1008...1011}{1007.1008.1009...1012}\)

\(=\frac{1006}{1012}=\frac{503}{506}\)

Answer 6

            Bài làm :

Ta có :

\(\left(1-\frac{1}{1007}\right)\left(1-\frac{1}{1008}\right)\left(1-\frac{1}{1009}\right)...\left(1-\frac{1}{1012}\right)\)

\(=\frac{1006}{1007}.\frac{1007}{1008}.\frac{1008}{1009}....\frac{1011}{1012}\)

\(=\frac{1006.1007.1008....1011}{1007.1008.1009....1012}\)

\(=\frac{1006}{1012}\)

\(=\frac{503}{506}\)