trả lời hộ tớ đi

Chi oi ,sao trung hop the!To cung ko giai dc

So sánh à bạn?

A=\(\frac{1}{2}\).\(\frac{2}{3}\)....\(\frac{2012}{2013}\)=\(\frac{1}{2013}\)

B=\(\frac{2012}{2012.2013}\)=\(\frac{1}{2013}\)

vậy A=B

\(A=\frac{1.2}{2.2}.\frac{2.3}{3.3}.\frac{3.4}{4.4}.\frac{4.5}{5.5}.....\frac{2012.2013}{2013.2013}=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}....\frac{2012}{2013}=\frac{1.2.3.4.5....2012}{2.3.4.5....2013}=\frac{1}{2013}\)

\(B=\frac{2012.2013-2012.2012}{2012.2011+2012.2}=\frac{2012.\left(2013-2012\right)}{2012.\left(2011+2\right)}=\frac{2012}{2012.2013}=\frac{1}{2013}\)

\(\Rightarrow A=B\)

a, \(A=\frac{2012\cdot2011-1}{2010\cdot2012+2011}=\frac{2012\cdot\left(2010+1\right)-1}{2010\cdot2012+\left(2012-1\right)}=\frac{2012\cdot2010+2012-1}{2012\cdot2010+2012-1}=1\)

b, 10,11 + 11,12 + 12,13 + .... + 97,98 + 98,99 + 99,100    

= ( 10 + 11 + 12 + .... + 97 + 98 + 99 ) + ( 0,10 + 0,11 + 0,12 + 0,13 + ... + 0,98 + 0,99 )

= { ( 10 + 99 ) . [ ( 99 - 10 ) : 1 + 1 ] ] : 2 } + { ( 0,10 + 0,99 ) . [ ( 0,99 - 0,10 ) : 0,01 + 1 ] : 2 }

= ( 99 . 90 : 2 ) + ( 1,09 . 90 : 2 )

= 4455 + 49,05

= 4504,05

\(S=\dfrac{1}{\sqrt{1.2012}}+\dfrac{1}{\sqrt{2.2011}}+...+\dfrac{1}{\sqrt{2012.1}}>\dfrac{1}{\dfrac{1+2012}{2}}+\dfrac{1}{\dfrac{2+2011}{2}}+...+\dfrac{1}{\dfrac{2012+1}{2}}=\dfrac{2012}{\dfrac{2013}{2}}=\dfrac{4024}{2013}\)

a) Ta có : \(\frac{2010}{2011}>\frac{2010}{2011+2012}\)

               \(\frac{2011}{2012}>\frac{2011}{2011+2012}\)

Nên \(\frac{2010}{2011}+\frac{2011}{2012}>\frac{2010+2011}{2011+2012}\)=> M > N

b) P = \(\frac{2011.2012-2}{2010.2011+4020}=\frac{2011.\left(2010+2\right)-2}{2010.2011+4020}=\frac{2011.2010+2011.2-2}{2010.2011+4020}=\)\(\frac{2011.2010+4020}{2010.2011+4020}=1\)

Nên P = 1

câu b sửa lại:\(P=\frac{2011.2012-2}{2010.2011+4020}=\frac{2011.2010+4022-2}{2010.2011+4020}=\frac{2010.2011+4020}{2010.2011+4020}=1\)

Ta có: \(\frac{2011\times2012-2}{2010\times2011+4020}=\frac{2011\times\left(2010+2\right)-2}{2010\times2011+4020}=\frac{2011\times2010+4022-2}{2010\times2011+4020}=\frac{2011\times2010+4020}{2010\times2011+4020}=1\)

Vậy \(\frac{2011\times2012-2}{2010\times2011+4020}=1\)

\(P=\frac{2011.2012-2}{2010.2011+4020}=\frac{2010.2011+2.2011-2}{2010.2011+4020}=\frac{2010.2011+4042-2}{2010.2011+4020}=\frac{2010.2011+4040}{2010.2011+4040}=1\)

Vậy P = 1

=1 nha ban

\(=\frac{2008+2009.2010}{2010.\left(2009+2\right)-2012}\)

\(=\frac{2009.2010+2008}{2010.2009+2010.2-2012}\)

\(=\frac{2008+2009.2010}{2008+2009.2010}=1\)

\(MS=2011.2013+2012\)

\(=\left(2012-1\right).2013+2012\)

\(=2012.2013-2013+2012\)

\(=2013.2012-1\)

\(=TS\)

Vậy phân số đã cho bằng 1.

Trả lời:

\(\frac{2013.2012-1}{2011.2013+2012}=\frac{2013.\left(2011+1\right)-1}{2011.2013+2012}\)

                                        \(=\frac{2011.2013+2013-1}{2011.2013+2012}\)

                                        \(=\frac{2011.2013+2012}{2011.2013+2012}\)

                                        \(=1\)

Học tốt

\(\frac{2013.2012-1}{2011.2013+2012}\)

\(=\frac{2013.2012-1}{2011.2013+2013-1}\)

\(=\frac{2013.2012-1}{2012.2013-1}\)

\(=1\)

\(\frac{2010\cdot2011+1000}{2012\cdot2010-1010}\)

= \(\frac{2010\cdot2011+1000}{\left(2011+1\right)\cdot2010-1010}\)

= \(\frac{2010\cdot2011+1000}{2011\cdot2010+2010-1010}\)

= \(\frac{2010\cdot2011+1000}{2011\cdot2010+1000}\)

= 1

\(\frac{2010.2011+1000}{2012.2010-1010}\)

\(=\frac{2010.2011+2010-1010}{2012.2010-1010}\)

\(=\frac{2010.\left(2011+1\right)-1010}{2012.2010-1010}\)

\(=\frac{2010.2012-1010}{2012.2010-1010}\)

\(=1\)

\(\frac{2010\cdot2011+1000}{2012\cdot2010-1010}\)= \(\frac{2010\cdot2011+1000}{2011\cdot2010+2010-1010}\)= \(\frac{2010\cdot2011+1000}{2011\cdot2010+1000}\)= 1