c\(\frac{\left(1+\frac{2012}{1}\right)\left(1+\frac{2012}{2}\right)....\left(1+\frac{2012}{1000}\right)}{\left(1+\frac{1000}{1}\right)\left(1+\frac{1000}{2}\right)....\left(1+\frac{1000}{2012}\right)}\)

\(\frac{\left(1+\frac{2012}{1}\right)\left(1+\frac{2012}{2}\right).......\left(1+\frac{2012}{100}\right)}{\left(1+\frac{1000}{1}\right)\left(1+\frac{1000}{2}\right).....\left(1+\frac{1000}{2012}\right)}\)

So sánh A=\(\frac{1000^{2012}+2}{1000^{2012}-1}\) và B= \(\frac{1000^{2012}}{1000^{2012}-3}\)

Rút gọn : 

a/ \(A=\frac{\frac{1}{19}+\frac{2}{18}+\frac{3}{17}+...+\frac{19}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{20}}\)

b/ \(B=\frac{\left(1+\frac{2012}{1}\right)\left(1+\frac{2012}{2}\right)...\left(1+\frac{2012}{1000}\right)}{\left(1+\frac{1000}{1}\right)\left(1+\frac{1000}{2}\right)...\left(1+\frac{1000}{2012}\right)}\)

Tinh     [(1+2012/1)*(1+2012/2)*(1+2012/3)*...*(1+2012/1000)]/[(1+1000/1)*(1+1000/2)*(1+1000/3)*...*(1+1000/2012)]

tính B=[(1+2012/1)+(1+2012/2)+(1+2012/3)+...+(1+2012/1000)]:[(1+1000/1)+(1+1000/2)+...+(1+1000/2012)]

tính: B=[(1+2012/1)+(1+2012/2)+....+(1+2012/1000)]:[(1+1000/1)+(1+1000/2)+....+(1+1000/2012)]

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Câu 1

Cho A= (1+2012/1)(1+2012/2)...(1+2012/1000)

B=(1+1000/1)(1+1000/2).....(1+1000/2012)

Tính \(\frac{A}{B}\)

Câu 2

cho E = 1/1.2 + 1/3.4 +1/5.6 +....+1/2013.2014

F= 1/1008.2014 + 1/1009,2013 +....+1/2014.1008

Tính \(\frac{E}{F}\)

(1+2012/1)(1+2012/2)(1+2012/3).......(1+2012/1000) 

(1+1000/1)(1+1000/2)..........(1+1000/2012)

Tính A