Question

so sánh 

a/\(\frac{2010}{2009}\)và\(\frac{2011}{2010}\)

b/\(\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+...................+\frac{1}{200}\)và 1

Answer 1

a, Xét 2010 . 2010 = (2009+1).2010 

= 2009.2010 +2010

= (2009.2010+2009)+1

= 2009.(2010+1)+1

= 2009.2011+1 

>= 2009.2010

=> 2010/2009 > 2011/2010

Tk mk nha

Answer 2

a, \(\frac{2010}{2009}\)và \(\frac{2011}{2010}\)

Ta có:

2010.2010 = ( 2009 + 1 ) . 2010

                  = 2009 . 2010 + 2010

                  = ( 2009 . 2010 + 2019 ) + 1

                  = 2019 . ( 2010 + 1 ) + 1

                  = 2019 . 2011 + 1

\(\Rightarrow\)\(\frac{2010}{2009}>\frac{2011}{2010}\)

b, \(\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+...........+\frac{1}{200}\)và 1

Ta có:

\(\frac{1}{101}< 1;\frac{1}{102}< 1;\frac{1}{103}< 1;........;\frac{1}{200}< 1\)

\(\Rightarrow\)\(\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+.............+\frac{1}{200}< 1\)