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( 35 x 18 - 9 x 70 ) x 2010 x 2011 x ... x 2020
= (35 x 18 - 9 x 35 x 2) x 2010 x 2011 x ... x 2020
= ( 35 x 18 - 18 x 35 ) x 2010 x 2011 x ... x 2020
= 35 x (18 - 18 ) x 2010 x 2011 x ... x 2020
= 35 x 0 x 2010 x 2011 x ... x 2020
= 0 x 2010 x 2011 x ... x 2020
= 0
a. 1⋅2⋅3+2⋅4⋅6+3⋅6⋅9+4⋅8⋅12
= 6+2⋅4⋅6+3⋅6⋅9+4⋅8⋅12
= 6+48+3⋅6⋅9+4⋅8⋅12
= 6+48+162+4⋅8⋅12
= 6+48+162+384
= 600
b . Ta có \(A=\frac{2010+2011}{2011+2012}=\frac{2010}{2011+2012}+\frac{2011}{2011+2012}.\)
Ta có : \(\frac{2010}{2011+2012}< \frac{2010}{2011}\) và \(\frac{2011}{2011+2012}< \frac{2011}{2012}\)
=> \(\frac{2010+2011}{2011+2012}< \frac{2010}{2011}+\frac{2011}{2012}\)
=> A < B
\(\left(1+\dfrac{1}{2010}\right)\times\left(1+\dfrac{1}{2011}\right)\times...\times\left(1+\dfrac{1}{2020}\right)\)
=\(\dfrac{2011}{2010}\times\dfrac{2012}{2011}\times...\times\dfrac{2021}{2020}\)
=\(\dfrac{2021}{2010}\)
a)
Ta có a > b vì b > 3 còn a < 3
b)
a. Ta có : 1/51 + 1/52 + 1/53 +...+ 1/60 < 1/51 x 10 < 1/50 x 10 = 1/5
=> 1/51 + 1/52 +1/53 +...+1/60 < 1/5
b. Ta có : 1/51 + 1/52 + 1/53 +...+ 1/60 > 1/60 x 10 = 1/6
=> 1/51 + 1/52 +1/53 +...+ 1/60 > 1/6
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$
( 35 x 18 - 9 x 70 ) x 2010 x 2011 x 2012 x ... x 2020
= 0 x 2010 x 2011 x 2012 x ... x 2020
= 0 nha !
(35*18-9*70)*2010*2011*.....*2020
=(630-630)*2010*........*2020
=0*2010*.........*2020
=0
CHÚC BẠN HỌC TỐT!