2006 x 125 + 1000 126 x 2006 − 1006 = 2006 x 125 + 1000 125 x 2006 − 2006 − 1006 = 2006 x 125 + 1000 125 x 2006 + 1000 = 1

\(\dfrac{2006.125+1000}{126.2006-1006}\)

\(=\)\(\dfrac{2006.125+1000}{(125+1).2006-1006}\)

\(=\)\(\dfrac{2006.125+1000}{125.2006+1.2006-1006}\)

\(=\)\(\dfrac{2006.125+1000}{125.2006+2006-1006}\)

\(=\)\(\dfrac{2006.125+1000}{125.2006+1000}\)

\(=\) 1

2006 x 125 + 1000/126 x 2006 - 1006

= 2006 . 125 + 1000/125 . 2006 + 1 .2006 - 1006

= 2006 . 125 + 100/125 . 2006 + 1000

= 1

2006 x 125 + 1000/126 x 2006 - 1006

= 2006 x 125 + 1000/125 x 2006 + 1 x 2006 - 1006

= 2006 x 125 + 1000/125 x 2006 + 1000

= 1

a, 2006 x 2004 - \(\frac{2}{1995}\) + 2004 x 2005 = 8038043,999

b, 2006 x 125 + \(\frac{1000}{126}\) x 2006 - 1006 = 265664,6349

c, A = 1991 x 1999

=> A = ( 1995 - 4 ) x ( 1995 + 4 )

     A = 1995 x ( 1995 + 4 ) - 4 x ( 1995 + 4 )

     A = 1995 x 1995 + 1995 x 4 - ( 4 x 1995 + 4 x 4 )

     A = 1995 x 1995 - 4 x 4

mà B = 1995 x 1995

Vậy A < B

d, Gọi giá trị biểu thức là C

C =  \(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}\) 

C x 2 = \(\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{96}\)

C x 2 = \(\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}\)

Vậy C x 2 - C = \(\left(\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}\right)-\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}\right)\)

                  C = \(\frac{2}{3}-\frac{1}{96}\) ( vì phân số nào có ở số bị trừ cũng có ở số trừ thì trừ hết rồi nên không còn )

                  C = \(\frac{21}{32}\)

A=1991x1999=(1995-4)1999=1995x1999-4x1999

B=1995x1995=1995x(1999-4)=1995x1999-1995x4>1995x1999-4x1999=A

vậy A<B

\(\frac{2006\times125+1000}{126\times2006-1006}=\frac{2006\times125+1000}{\left(125+1\right)\times2006-1006}=\frac{2006\times125+1000}{2006\times125+2006\times1-1006}\)

\(=\frac{2006\times125+1000}{2006\times125+1000}=1\)

\(\frac{2006.125+1000}{126.2006-1006}=\frac{2006.125+1000}{\left(125+1\right).2006-1006}=\frac{2006.125+1000}{125.2006+1.2006-1006}=\frac{2006.125+1000}{125.2006+1000}=1\)

\(\frac{2006\times125+1000}{126\times2006-1006}=\frac{2006\times125+1000}{2006\times125+2006-1006}=\frac{2006\times125+1000}{2006\times125+1000}=1\)

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