1 1999/1)*(1 1999/2)

72/100

Tính \(\left( {1 + \frac{{1999}}{1}} \right)\left( {1 + \frac{{1999}}{2}} \right)...\left( {1 + \frac{{1999}}{{1000}}} \right):\left( {1 + \frac{{1000}}{1}} \right)\left( {1 + \frac{{1000}}{2}} \right)...\left( {1 + \frac{{1000}}{{1999}}} \right)\)

Nhập câu trả lời ở đây

0/3000 ký tự

Giải thích

Lời giải:

\(\left( {1 + \frac{{1999}}{1}} \right)\left( {1 + \frac{{1999}}{2}} \right)...\left( {1 + \frac{{1999}}{{1000}}} \right):\left( {1 + \frac{{1000}}{1}} \right)\left( {1 + \frac{{1000}}{2}} \right)...\left( {1 + \frac{{1000}}{{1999}}} \right)\)

= \(\frac{{2000}}{1}.\frac{{2001}}{2}...\frac{{2999}}{{1000}}:\left( {\frac{{1001}}{1}.\frac{{1002}}{2}...\frac{{2999}}{{1999}}} \right)\)

\( = \frac{{2000.2001...2999}}{{1.2...1000}}.\frac{{1.2...1999}}{{1001.1002...2999}}\)

= 1.