Bài 1: a) 1/5-1/7+4/5-12/14+1/2020
b) 2/1nhân3+2/3.5+2/5.7+…+2/2019.2020
c) -3/19 nhân -14/5 nhân 38/9 nhân 15/7
d) (1-1/2) nhân (1-2/4) nhân (1-2/6) nhân…nhân (1-2/2018) nhân (1-2/2020)
Bài 2: Cho x,y thuộc Q và x
Bài 1: a) 1/5-1/7+4/5-12/14+1/2020
b) 2/1nhân3+2/3.5+2/5.7+…+2/2019.2020
c) -3/19 nhân -14/5 nhân 38/9 nhân 15/7
d) (1-1/2) nhân (1-2/4) nhân (1-2/6) nhân…nhân (1-2/2018) nhân (1-2/2020)
Bài 2: Cho x,y thuộc Q và x
B1,
a, 1/5-1/7+4/5-12/14+1/2020
=(1/5+4/5)-1/7-12/14+1/2020
=1+(-1/7-12/14)+1/2020
=1+(-1)+1/2020
=0+1/2020
=1/2020
c, -3/19.(-14/5)/38/9.15/7
=-3/19.38/9.(-14/5).15/7
=$\frac{-3.38}{19.9}.\frac{-14.15}{5.7}$
=-2/3.(-6)
=12/3=4
……….
Giải thích các bước giải:
Bài 1:
a) $\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{4}{5}-\dfrac{12}{14}+\dfrac{1}{2020}\\=\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{4}{5}-\dfrac{6}{7}+\dfrac{1}{2020}\\=\bigg(\dfrac{1}{5}+\dfrac{4}{5}\bigg)-\bigg(\dfrac{1}{7}+\dfrac{6}{7}\bigg)+\dfrac{1}{2020}\\= 1-1 + \dfrac{1}{2020}=\dfrac{1}{2020}$
b) (Mik sửa lại đề chút nhé bn!)
$\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+…+\dfrac{2}{2019.2021}\\= 1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+…+\dfrac{1}{2019}-\dfrac{1}{2021}\\= 1-\dfrac{1}{2021}=\dfrac{2020}{2021}$
c) $\dfrac{-3}{19}.\dfrac{-14}{5}.\dfrac{38}{9}.\dfrac{15}{7}\\=\dfrac{-3.(-14).38.15}{19.5.9.7}\\=\dfrac{3.14.38.15}{19.5.9.7}\\= \dfrac{3.2.7.2.19.3.5}{19.5.3.3.7}=2.2=4$
d) $\bigg(1-\dfrac{1}{2}\bigg).\bigg(1-\dfrac{2}{4}\bigg).\bigg(1-\dfrac{2}{6}\bigg)…\bigg(1-\dfrac{2}{2018}\bigg).\bigg(1-\dfrac{2}{2020}\bigg)\\=\dfrac{1}{2}.\dfrac{1}{2}.\dfrac{2}{3}…\dfrac{1008}{1009}.\dfrac{1009}{1010}\\=\dfrac{1}{2}.\dfrac{1.2…1008.1009}{2.3…1009.1010}\\=\dfrac{1}{2}.\dfrac{1}{1010}=\dfrac{1}{2020}$
Bài 2:
$x<y⇔ xy+10x<xy+10y\\⇔x(y+10)<y(x+10)\\⇔\dfrac{x}{y}<\dfrac{x+10}{y+10}$