Gọi 123456788 là A

\(123456789=a+1\)

\(123456787=a-1\)

\(A=\left(a+1\right).\left(a-1\right)\)

\(A=a^2-a+a-1\)

\(A=a^2-1\)

\(Vì:a^2-1< a^2\Leftrightarrow A< B\)

123456789 (có 9 chữ số) < 10^9 (10 chữ số) < 81^9 = 9^18 
=> 123456789^9 < 9^(18*9) < 9^(123456789) 

Ta co: \(M=\frac{2013}{123456789}+\frac{2014}{987654321}=\frac{2013}{123456789}+\frac{2013}{987654321}+\frac{1}{987654321}\)

\(N=\frac{2013}{123456789}+\frac{1}{123456789}+\frac{2013}{987654321}\)

ma \(\frac{1}{987654321}< \frac{1}{123456789}\) nen \(M< N\)

\(M=\frac{2013}{123456789}+\frac{2014}{987654321}\)

\(N=\frac{2014}{123456789}+\frac{2013}{987654321}\)

\(M=\frac{2014}{987654321}-\frac{1}{987654321}\)

\(N=\frac{2014}{123456789}-\frac{1}{123456789}\)

Ta thấy \(\frac{1}{123456789}>\frac{1}{987654321}\)

\(\Rightarrow M< N\)

Ta có

\(A=\frac{2011}{123456789}+\frac{2011}{987654321}+\frac{1}{987654321}\)

\(B=\frac{2011}{123456789}+\frac{1}{123456789}+\frac{2011}{987654321}\)

Mặt khác

\(\frac{1}{987654321}< \frac{1}{123456789}\)

\(\Rightarrow\frac{2011}{123456789}+\frac{2011}{987654321}+\frac{1}{987654321}< \frac{2011}{123456789}+\frac{1}{123456789}+\frac{2011}{987654321}\)

=> A<B

\(A=123456789.123456789\)

\(B=123456788.123456790\)

Ta có: B=123456788*123456790

          <=>B=(123456789-1)(123456789+1)

                   =123456789^2-1<123456789
Hay B<A

123456789.123456789

123456789.123456789

So sánh A và B biết :

A = a^a^9 = a^9.a

B = 9^9^a = 9^9.a

Đây là hai lũy thừa cùng số mũ 

mà a = 123456789 > 9 suy ra A > B  nhé

A > B nhá ^_^"

I don't now 

sorry 

...................

nha

123456789⁹ > 9^123456789  

^{bai nay la toan do nhe ! neu thay dung k cho minh nhe}

\(123456789^9< 9^{123456789}\)

ko tin lấy máy tính thử đi

123456789 , ta co:

2014^9^9^123456789 & 2015^123456789^123456789^9

ta thay 2014 <2015   \  9<1...9   \9< 1...9

nen 2014^9^9^a < 2015^a^a^9

vi may minh mat vietkey nen khong dang dau thong cam