CMR: A=1.2.3...2012(1+\(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}⋮2012\))

1. Cho A= 1.2.3...2012.\(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}\right)\)

CMR: A chia hết cho 2013

Chứng minh 1.2.3...2012. ( 1 +\(\frac{1}{2}\)+\(\frac{1}{3}\)+...+\(\frac{1}{2012}\)) chia hết cho 13

Cho B=1.2.3.....2012.(1+\(\frac{1}{2}\)+\(\frac{1}{3}\)+....+\(\frac{1}{2012}\))

CTR B\(⋮\)2013

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

\(\frac{1+\frac{1}{2}+\frac{1}{3}+....\frac{1}{2012}}{\frac{2013}{1}+\frac{2014}{2}+\frac{2015}{3}....\frac{4024}{2012}-2012}\)

tính nhanh cả nhà ơi

Tìm x biết:

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

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

Tìm x biết:

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

  bài 1 :a) Tính M:\(\frac{\frac{7}{2012}+\frac{7}{9}-\frac{1}{4}}{\frac{5}{9}-\frac{3}{2012}-\frac{1}{2}}\)

          b) So sánh A và B biết A =\(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2010}\);;; B =\(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+....+\frac{1}{17}\)