B= 1/2 x 2/3 x 3/4 x ...........x 2002/2003 x 2003/2004

1 x 2 x 3 x 4 x .............x 2002 x 2003

2 x 3 x 4 x .............x 2003 x 2004

1

 2004

x²-9-(-2)²=4x10+2³

x²-9-4=40+8

x²     =40+8+4+9=61

x=\(\sqrt{61}\)

Đặt \(A=\dfrac{2}{1.5}+\dfrac{3}{5.11}+\dfrac{4}{11.19}+\dfrac{5}{19.29}+\dfrac{6}{29.41}\)

\(2A=\dfrac{4}{1.5}+\dfrac{6}{5.11}+\dfrac{8}{11.19}+\dfrac{10}{19.29}+\dfrac{12}{29.41}\)

\(2A=\dfrac{1}{1}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{41}\)

\(2A=\dfrac{1}{1}-\dfrac{1}{41}=\dfrac{40}{41}\)

\(A=\dfrac{40}{41}:2=\dfrac{20}{41}\)

Đặt \(B=\dfrac{1}{1.4}+\dfrac{2}{4.10}+\dfrac{3}{10.19}+\dfrac{4}{19.31}\)

Tương tự ta dễ dàng tình đc:

\(B=\dfrac{10}{31}=\dfrac{20}{62}\)

Ta có: \(\dfrac{20}{41}< \dfrac{20}{62}\Rightarrow A< B\)

Vậy ........................

Chúc bn học tốt

Đặt A=2/1.5+3/5.11+...+6/29.41

B=1/1.4+2/4.10+3/10.19+4/19.31

2A=4/1.5+6/5.11/+...+12/29.41

2A=1-1/5+1/5-1/11+...+1/29-1/41

2A=1-1/41

2A=40/41

A=20/41

3B=3/1.4+6/4.10+9/10.19+12/19.31

3B=1-1/4+1/4-1/10+1/10-1/19+1/19-1/31

3B=1-1/31

3B=30/31

B=10/31

Vì 10/31<20/41 nên B<A

\(a.\frac{19}{13}+\frac{-7}{11}+\frac{-4}{11}-\frac{6}{13}\)

\(=\left(\frac{19}{13}-\frac{6}{13}\right)+\left(\frac{-7}{11}+\frac{-4}{11}\right)\)

\(=1+\left(-1\right)\)

\(=0\)

(19/13-6/13)+(-7/11+-4/11)

1+-1

0