Đặt A=\(1+2+2^2+........+2^{2008}\)
2A=\(2+2^2+2^3+.............+2^{2009}\)
=>A-2A=\(\left(1+2+2^2+.........+2^{2008}\right)-\left(2+2^2+2^3+..........+2^{2009}\right)\)
=>\(-A=1-2^{2009}\)
=>\(A=-\left(1-2^{2009}\right)\)
=>\(M=\frac{-\left(1-2^{2009}\right)}{1-2^{2009}}\)
=>\(M=-1\)
Tính B =\(\frac{1+2+2^2+2^3+...+2^{2008}}{1-2^{2009}}\)
Tính : \(B=\frac{1+2+2^2+2^3+......+2^{2008}}{1-2^{2009}}\)
so sánh 2 phân số : \(A=\frac{2008^{2009}+2}{2008^{2009}-1};B=\frac{2008^{2009}}{2008^{2009}-3}\)
a, Tính nhanh :
\(\frac{2009\times(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2007}+\frac{1}{2008})}{2008-\left(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{2006}{2007}+\frac{2007}{2008}\right)}\)
b, Cho \(\text{Q}=2+2^2+2^3+...+2^{10}\). Chứng tỏ rằng \(Q⋮3\).
Tính \(B=\frac{1+2+2^2+2^3...+2^{2008}}{1-2^{2009}}\)
Tính \(B=\frac{1+2^2+2^3+...+2^{2008}}{1-2^{2009}}\)
tính:
B=
\(y=\frac{1+2+2^2+2^3+....+2^{2008}}{1-2^{2009}}\frac{ }{ }\)
Tính nhanh:
\(B=\frac{1+2+2^2+2^3+...+2^{2008}}{1-2^{2009}}\)
1. \(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{99}}+\frac{1}{2^{100}}+\frac{1}{2^{100}}\)
2. So sánh: \(\dfrac{2008}{2009}+\dfrac{2009}{2010}\) và \(\dfrac{2008+2009}{2009+2010}\)
