Tìm x, biết
a) \(\frac{1}{2}.x+\frac{3}{5}.x=\frac{-2}{3}\)
b) \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}=\frac{2020}{2021}\)
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\(\left(-\frac{7}{24}-0,75+25\%\right):\left(-2\frac{1}{8}\right)\)
\(=\left(-\frac{7}{24}-\frac{18}{24}+\frac{6}{24}\right):\left(-\frac{17}{8}\right)\)
\(=\left(-\frac{19}{24}\right)\cdot\left(-\frac{8}{17}\right)\)
\(=\frac{19}{51}\)
Vì a;b;c > 0 => \(\frac{a}{c+a}< \frac{a+b}{a+b+c}\) ;
\(\frac{b}{a+b}< \frac{b+c}{a+b+c}\);
\(\frac{c}{b+c}< \frac{a+c}{a+b+c}\)
Khi đó \(\frac{a}{c+a}+\frac{b}{a+b}+\frac{c}{b+c}< \frac{a+b}{a+b+c}+\frac{b+c}{a+b+c}+\frac{c+a}{a+b+c}\)
\(=\frac{a+b+b+c+c+a}{a+b+c}=\frac{2\left(a+b+c\right)}{a+b+c}=2\)(đpcm)
\(\frac{1}{2.5}\)\(+\)\(\frac{1}{5.8}\)\(+\frac{1}{8.11}\)\(+...+\frac{1}{152.155}\)
=\(\frac{1}{2}\) \(-\frac{1}{5}\) \(+\frac{1}{5}\) \(-\frac{1}{8}\) \(+...+\frac{1}{152}\) \(-\frac{1}{155}\)
=\(\frac{1}{2}\)\(-\frac{1}{155}\)
=\(\frac{153}{310}\)
a) \(A=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{4}-1\right)....\left(\frac{1}{1000}-1\right)=-\frac{1}{2}.\left(-\frac{2}{3}\right).\left(-\frac{3}{4}\right)...\left(-\frac{999}{1000}\right)\)
\(=-\frac{1.2.3...999}{2.3.4...1000}=-\frac{1}{1000}\)
b)\(B=\frac{\frac{3}{5}+\frac{3}{7}-\frac{3}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{11}}:\frac{3}{4}=\frac{3\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}{4\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}:\frac{3}{4}=\frac{3}{4}:\frac{3}{4}=1\)
d) \(D=1+\frac{1}{2}+\frac{1}{4}+..+\frac{1}{512}+\frac{1}{1024}\)
=> \(2D=2+1+\frac{1}{2}+...+\frac{1}{256}+\frac{1}{512}\)
=> \(2D-D=\left(2+1+\frac{1}{2}+...+\frac{1}{256}+\frac{1}{512}\right)-\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{512}+\frac{1}{1024}\right)\)
=> \(D=2-\frac{1}{1024}=\frac{2047}{1024}\)
Câu 3. Đúng ghi Đ, sai ghi S.
a) 2,3 giờ < 2 giờ 30 phút s
c) 125 x 0,8 > 100 s
b) 3 m2 6 dm2 = 3,06 m2 đ
d) 5 kg = 0,05 tạ đ
a) 1/2. X+ 3/5. X = -2/3
X. (1/2 +3/5)= -2/3
X. 11/10= -2/3
X= -2/3 :11/10
X= -20/33
b) 1/1.2 + 1/2.3 + 1/3.4 +......+ 1/x.(x+1)=2020/2021
1-1/2+1/2-1/3+1/3-1/4+.....+1/x-1/x+1=2020/2021
1-1/x+1=2020/2021
1/x+1= 1-2020/2021
1/x+1=1=1/2021
=>x+1=2021 =>x=2020
Vậy x=2020
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