|3x+5y-2|+|3y-8z+5|+|4z-x+10|=2020²⁰¹⁹

^{tìm x,y,z thuộc Z}

|x+1|+|y-2|+(z-5)²⁰≤0

tìm x,y,z

E=\(\dfrac{\dfrac{2}{15}-\dfrac{2}{21}+\dfrac{2}{39}}{\dfrac{5}{20}-\dfrac{5}{28}+\dfrac{5}{52}}\)

E=\(\dfrac{2.\dfrac{1}{3}.\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{13}\right)}{5.\dfrac{1}{4}.\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{13}\right)}\)

E=\(\dfrac{2.\dfrac{1}{3}}{5.\dfrac{1}{4}}\)

E=8/15

1.21​+3.41​+5.61​+...+49.501​

=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{49}-\frac{1}{50}=1−21​+31​−41​+51​−61​+...+491​−501​

=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{49}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{50}\right)=(1+31​+51​+...+491​)−(21​+41​+61​+...+501​)

=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{50}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{50}\right)=(1+21​+31​+...+501​)−2(21​+41​+61​+...+501​)

=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{50}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{25}\right)=(1+21​+31​+...+501​)−(1+21​+31​+...+251​)

=\frac{1}{26}+\frac{1}{27}+\frac{1}{28}+...+\frac{1}{50}=261​+271​+281​+...+501​
=> đpcm

Cho △ABC có góc ABC=50 Độ, góc ACB=20 độ. Ax là tia đối của Ac.

a) Tính góc BAx

b) Kẻ BH vuông góc với Ax(HϵAx) . Tính  gócHBA

c) vẽ Cy sao cho CA là tia pg của góc BCy. tia Cy cắt AB kéo dài tại M .Chứng minh CM vuông góc với BM