Ta có : B = 1.2.3.....671......2012(1 + \(\frac{1}{2}+\frac{1}{3}+.......+\frac{1}{2012}\))
<=> B = 1.2.4........672......2012.2013((1 + \(\frac{1}{2}+\frac{1}{3}+.......+\frac{1}{2012}\)) chai hết cho 2013
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
cho so A=\(\frac{2013+\frac{1}{2}}{\left(2012+\frac{1}{2}\right)^2+2013+\frac{1}{2}}\)
B=\(\frac{2013+\frac{1}{3}}{\left(2012+\frac{1}{3}\right)^2+2013+\frac{1}{3}}\)
so sanh A va B
\(B=\frac{1-3}{1\cdot3}+\frac{2-4}{2\cdot4}+\frac{3-5}{3\cdot5}+\frac{4-6}{4\cdot6}+............+\frac{2011-2013}{2011.2013}+\frac{2012-2014}{2012\cdot2014}-\frac{2013+2014}{2013\cdot2014}\)
CMR: A=1.2.3...2012(1+\(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}⋮2012\))
So sánh:
A = \(\frac{2012^{2013}+2}{2012^{2013}-1}\)
B=\(\frac{2012^{2013}}{2012^{2013}-3}\)
So sánh:
A = \(\frac{2012^{2013}+2}{2012^{2013}-1}\)
B=\(\frac{2012^{2013}}{2012^{2013}-3}\)
Tìm x biết:
a) \(^{2^x+2^{x+1}+2^{x+2}+2^{x+3}=480}\)
b) \(\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}+\frac{1}{2013}\right).x=\frac{2012}{1}+\frac{2011}{2}+\frac{2010}{3}+...+\frac{2}{2011}+\frac{1}{2012}\)
So sánh:
a) \(\frac{2^{10}+1}{2^{10}-1}\)và \(\frac{2^{10}-1}{2^{10}-3}\)
b) \(\frac{2011}{2012}+\frac{2012}{2013}\)và \(\frac{2011+2012}{2012+2013}\)
Tính giá trị biểu thức B=\(2013+\frac{2013}{1+2}+\frac{2013}{1+2+3}+\frac{2013}{1+2+3+4}+...+\frac{2013}{1+2+3+...+2012}\)
