Ta thấy 

\(\dfrac{2010}{2011}< 1\)

\(\dfrac{2011}{2012}< 1\)

\(\dfrac{2012}{2013}< 1\)

\(\dfrac{2013}{2014}< 1\) 

=> Tổng M của những phân số trên sẽ nhỏ hơn 1 

=> M < 1

\(\dfrac{2010}{2011}+\dfrac{2011}{2012}+\dfrac{2012}{2013}+\dfrac{2013}{2011}\)

=1-\(\dfrac{1}{2011}\)+1\(-\dfrac{1}{2012}\)+1-\(\dfrac{1}{2013}\)+1-\(\dfrac{1}{2011}\)

=4-(\(\dfrac{2}{2011}+\dfrac{1}{2012}+\dfrac{1}{2013}\)) < 4 

m=\(\dfrac{2010}{2011}+\dfrac{2011}{2012}+\dfrac{2012}{2013}+\dfrac{2013}{2011}\)

=\(1-\dfrac{1}{2011}+1-\dfrac{1}{2012}+1-\dfrac{1}{2013}+1+\dfrac{2}{2011}\)

=4+\(\dfrac{1}{2011}-\dfrac{1}{2012}-\dfrac{1}{2013}\)

vì:

do \(\dfrac{1}{2011}< 1\)

\(\dfrac{1}{2012}< 1\)

\(\dfrac{1}{2013}< 1\)

nên \(\dfrac{1}{2011}-\dfrac{1}{2012}-\dfrac{1}{2013}< 1-1-1=-1\)

hay \(\dfrac{1}{2011}-\dfrac{1}{2012}-\dfrac{1}{2013}< 0\)

nên 4+\(\dfrac{1}{2011}-\dfrac{1}{2012}-\dfrac{1}{2013}< 4\)

vậy tổng m <4

bài này mình tưởng phải lên cấp 2 mới có thế mà mấy em lớp 4 đã phải làm á

????

Vì 2011²⁰¹¹<2011²⁰¹² =>2011²⁰¹¹ +1<2011²⁰¹² +1

=>  2011²⁰¹¹+1/2011²⁰¹²+1 <1

=>B<1

=>B=2011²⁰¹¹+1/2011²⁰¹²+1<2011²⁰¹¹+1+2010/2011²⁰¹²+1+2010

=>B<2011²⁰¹¹+2011/2011²⁰¹²+2011=2011²⁰¹⁰.2011+2011/2011²⁰¹¹.2011+2011=2011.(2011²⁰¹⁰+1)/2011.(2011²⁰¹¹+1)

=>B<2011²⁰¹⁰+1/2011²⁰¹¹+1=A

=>B<A

Vậy B<A

M<4 :)

với cả đây là bài lớp 5

m bé hơn 4

mà giờ lớp 4 học khó nhở

M=2010/2011+2011/2012+2012/2013+2013/2014
4 = 1+1+1+1
Mà 2010/2011 <1
2011/2012<1
2012/2013<1
2013/2014 <1
=>2010/2011+2011/2012+2012/2013+2013/2014​ < 1+1+1+1 
=> M<4

tích cho chị zới nha

nhận xét

\(\dfrac{2010}{2011}\)<1

...

\(\dfrac{2013}{2014}< 1\)

vì 1<4⇒M<4

\(\frac{2010}{2011}\)+\(\frac{2011}{2012}\)+\(\frac{2012}{2013}\)+\(\frac{2013}{2011}\)

= 1 -\(\frac{1}{2011}\)+ 1 -\(\frac{1}{2012}\)+ 1 -\(\frac{1}{2013}\)+ 1 + \(\frac{2}{2011}\)

= 4 + \(\frac{1}{2011}\)-\(\frac{1}{2012}\)-\(\frac{1}{2013}\)< 4

$\frac{2010}{2011}$+$\frac{2011}{2012}$+$\frac{2012}{2013}$+$\frac{2013}{2011}$

= 1 -$\frac{1}{2011}$+ 1 -$\frac{1}{2012}$+ 1 -$\frac{1}{2013}$+ 1 + $\frac{2}{2011}$

= 4 + $\frac{1}{2011}$-$\frac{1}{2012}$-$\frac{1}{2013}$< 4

Ta có :

B = \(\dfrac{2011}{2012}\) + \(\dfrac{2012}{2013}\) .

       \(\dfrac{2011}{2012}\) > \(\dfrac{2011}{2012+2013}\) .

        \(\dfrac{2012}{2013}\) > \(\dfrac{2012}{2012+2013}\) .

\(\Rightarrow\) A < B .

Ta có :

B = 2012201320122013 .

       20112012+201320112012+2013 .

        20122012+201320122012+2013 .

 A < B .

Giải:

Ta có:

\(A=\dfrac{2011+2012}{2012+2013}\) 

\(A=\dfrac{2011}{2012+2013}+\dfrac{2012}{2012+2013}\) 

Vì \(\dfrac{2011}{2012}>\dfrac{2011}{2012+2013}\)  

\(\dfrac{2012}{2013}>\dfrac{2012}{2012+2013}\)

\(\Rightarrow A< B\)

Câu trả lời:A<B