Question

[Kan]

Rút gọn: 

\(P=\frac{\left(1+\frac{2007}{1}\right)\left(1+\frac{2007}{2}\right)....\left(1+\frac{2007}{1000}\right)}{\left(1+\frac{1000}{1}\right)\left(1+\frac{1000}{2}\right)....\left(1+\frac{1000}{2007}\right)}\)

Answer 1

[Cậu chủ họ Lương]

tử số= (2008.2009....3007)/(1.2....1000)

mấu số=(1001.1002.....3007)/(1.2.3.....2007)

Chia cho nhau thì =1

chúc bạn học tốt

HYC-29/1/2022

Answer 2

[Xyz OLM]

\(P=\frac{\left(1+\frac{2007}{1}\right).\left(1+\frac{2007}{2}\right)...\left(1+\frac{2007}{1000}\right)}{\left(1+\frac{1000}{1}\right)\left(1+\frac{1000}{2}\right)...\left(1+\frac{1000}{2007}\right)}\)

\(=\frac{\frac{2008}{1}.\frac{2009}{2}...\frac{3007}{1000}}{\frac{1001}{1}.\frac{1002}{2}...\frac{3007}{2007}}=\frac{\frac{2008.2009....3007}{1.2....1000}}{\frac{1001.1002..3007}{1.2...2007}}\)

\(=\frac{2008.2009....3007}{1.2.3...1000}.\frac{1.2.3...2007}{1001.1002...3007}=\frac{3007!}{3007!}=1\)