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

\(S=\sqrt{1+2010^2+\frac{2010^2}{2011^2}}+\frac{2010}{2011}+\sqrt{1+2011^2+\frac{2011^2}{2012^2}}+\frac{2011}{2012}+\sqrt{1+2012^2+\frac{2012^2}{2013^2}}+\frac{2012}{2013}\)

bai 1:tính nhanh : P=\(\frac{\frac{2}{3}-\frac{1}{4}+\frac{5}{11}}{\frac{5}{12}+1-\frac{7}{11}}\)

Bai 2:Thực hiện phép tính: 1-2+3-4+5-6+...+2011-2012

Bai 3:so sánh:A=\(\frac{2011+2012}{2012+2013}\)

              B=\(\frac{2011}{2012}+\frac{2012}{2013}\)

bai4:so sánh:A=\(\frac{20^{10}+1}{20^{10}-1}\)

             B=\(\frac{20^{10}-1}{20^{10}-3}\)

Rút gọn:

A =\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)\)

B = \(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\)

So sánh :

\(A=\frac{20^{10}+1}{20^{10}-1}vàB=\frac{20^{10}-1}{20^{10}-3}\)

Tinh cach bieu thuc sau

A=2+4-6-8+10+12-14-16+....+210+214-216-218

B=\(2^{2013}-2^{2012}-2^{2011}-2^{2010}-...-2-1\)

C=\(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}\)

Tìm x biết:

a) \(^{2^x+2^{x+1}+2^{x+2}+2^{x+3}=480}\)

b) \(\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}+\frac{1}{2013}\right).x=\frac{2012}{1}+\frac{2011}{2}+\frac{2010}{3}+...+\frac{2}{2011}+\frac{1}{2012}\)

Tính \(\sqrt{1^3+2^3+....+2011^3+2012^3}\)

Cho đa thức P(x) =  \(\frac{1}{x^2+x}+\frac{1}{x2+3x+2}+\frac{1}{x^2+5x+6}+\frac{1}{x^2+7x+12}+\frac{1}{x^2+9x+20}\)Tính P(0,9)

Tìm x biết:

a) \(^{2^x+2^{x+1}+2^{x+2}+2^{x+3}=480}\)

b) \(\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}+\frac{1}{2013}\right).x=\frac{2012}{1}+\frac{2011}{2}+\frac{2010}{3}+...+\frac{2}{2011}+\frac{1}{2012}\)