ta có 

\(a=1+3^2+3^4+..+3^{2008}\)

\(\Rightarrow9a=3^2+3^4+..+3^{2010}\) lấy hiệu hai phương trình ta có

\(8a=3^{2010}-1\Rightarrow a=\frac{3^{2010}-1}{8}=b\)

khó wá bn

Ta có: \(\sqrt{1}< \sqrt{2};\sqrt{3}< \sqrt{4};\sqrt{5}< \sqrt{6};...;\sqrt{2009}< \sqrt{2010}\)

\(\Rightarrow\sqrt{1}+\sqrt{3}+\sqrt{5}+...+\sqrt{2009}< \sqrt{2}+\sqrt{4}+\sqrt{6}+...+\sqrt{2010}\)

\(\Rightarrow2\left(\sqrt{1}+\sqrt{3}+\sqrt{5}+...+\sqrt{2009}\right)< 2\left(\sqrt{2}+\sqrt{4}+\sqrt{6}+...+\sqrt{2010}\right)\)

\(\Rightarrow2\sqrt{1}+2\sqrt{3}+2\sqrt{5}+...+2\sqrt{2009}< 2\sqrt{2}+2\sqrt{4}+2\sqrt{6}+...+2\sqrt{2010}\)

Vậy A < B.

Dễ thấy: \(2008^3+1>0\); \(2008^2-2007>0\)

Nên \(\frac{2008^3+1}{2008^2-2007}>0\Leftrightarrow A>0\)

và \(2009-2010< 0\); \(2009^3-1>0\)

\(\Rightarrow\frac{2009^3-1}{2009-2010}< 0\Leftrightarrow B< 0\)

Vậy A > B

a hon b nhe thanh ha

DỄ VÃI CHƯỞNG

Dễ mà ko làm được thì nghỉ học đi 

mik tính A trước nhé

\(A=1-2+2^2-...-2^{2007}+2^{2008}\)

\(2.A=2-2^2+2^3-...-2^{2008}+2^{2009}\)

\(2.A-A=\left(2-2^2+2^3-..-2^{2008}+2^{2009}\right)\)\(-\left(1-2+2^2-...-2^{2007}+2^{2008}\right)\)

\(A=1-2^{2009}\)

Ta có:

$S=\dfrac{5}{1\cdot2\cdot3}+\dfrac{8}{2\cdot3\cdot4}+\dfrac{11}{3\cdot4\cdot5}+\cdots+\dfrac{6026}{2008\cdot2009\cdot2010}$

Nhận thấy tử số có dạng $3n+2$, nên:

$S=\sum_{n=1}^{2008}\dfrac{3n+2}{n(n+1)(n+2)}$

Ta có: $\dfrac{3n+2}{n(n+1)(n+2)}=\dfrac{1}{n(n+1)}+\dfrac{2}{(n+1)(n+2)}$

Do đó:

$S=\left(\dfrac1{1\cdot2}+\dfrac1{2\cdot3}+\cdots+\dfrac1{2008\cdot2009}\right)$

$+2\left(\dfrac1{2\cdot3}+\dfrac1{3\cdot4}+\cdots+\dfrac1{2009\cdot2010}\right)$

Mà: $\dfrac1{n(n+1)}=\dfrac1n-\dfrac1{n+1}$

Nên: $S=\left(1-\dfrac1{2009}\right)+2\left(\dfrac12-\dfrac1{2010}\right)$

$=1-\dfrac1{2009}+1-\dfrac1{1005}$

$=2-\dfrac1{2009}-\dfrac1{1005}$

Vì: $\dfrac1{2009}+\dfrac1{1005}>0$

Nên $S<2$