b) \(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{499}{1000}\)

\(\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{499}{1000}\)

\(\dfrac{2}{2.3}+\dfrac{2}{3.4}+\dfrac{2}{4.5}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{499}{1000}\)

mik lỡ bấm nhầm rồi, phần sau bn tự nghĩ nhé, sorry

b)\(\dfrac{2}{6}\)+\(\dfrac{2}{12}\)+.......+\(\dfrac{2}{x.\left(x+1\right)}\)=\(\dfrac{499}{1000}\)

\(\dfrac{2}{2.3}\)+\(\dfrac{2}{3.4}\)+.........+\(\dfrac{2}{x.\left(x+1\right)}\)=\(\dfrac{499}{1000}\)

2.(\(\dfrac{1}{2.3}\)+\(\dfrac{1}{3.4}\)+.........+\(\dfrac{1}{x.\left(x+1\right)}\))=\(\dfrac{499}{1000}\)

2.(\(\dfrac{1}{2}\)-\(\dfrac{1}{3}\)+\(\dfrac{1}{3}\)-..........+\(\dfrac{1}{x}\)-\(\dfrac{1}{x+1}\))=\(\dfrac{499}{1000}\)

2.(\(\dfrac{1}{2}\)-\(\dfrac{1}{x+1}\))=\(\dfrac{499}{1000}\)

\(\dfrac{1}{2}\)-\(\dfrac{1}{x+1}\)=\(\dfrac{499}{1000}\):2

\(\dfrac{1}{2}\)-\(\dfrac{1}{x+1}\)=\(\dfrac{499}{2000}\)

\(\dfrac{1}{x+1}\)=\(\dfrac{1}{2}\)-\(\dfrac{499}{2000}\)

\(\dfrac{1}{x+1}\)=\(\dfrac{501}{2000}\)

Đề bài sai phải

1> a) \(\frac{5}{7}x4:\frac{5}{9}=\frac{5}{7}:\frac{5}{9}x4=\frac{5}{7}x\frac{9}{5}x4=\frac{9}{7}x4=\frac{9x4}{7}=\frac{36}{7}\)

\(b,8x\frac{2}{3}:\frac{1}{2}=8x\frac{2}{3}x\frac{2}{1}=8x2x\frac{2}{3}=16x\frac{2}{3}=\frac{32}{3}\)

\(c,6:\frac{3}{5}-\frac{7}{6}x\frac{6}{7}=6x\frac{5}{3}-1=10-1=9\)

\(\frac{21}{5}x\frac{10}{11}+\frac{57}{11}=\frac{42}{11}+\frac{57}{11}=\frac{99}{11}=9\)

2) a) \(\frac{35}{9}:x=\frac{35}{6}\)

\(x=\frac{35}{9}:\frac{35}{6}\)

\(x=\frac{35}{9}x\frac{6}{35}\)

\(x=\frac{2}{3}\)

b) \(\left(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}\right)x10-X=0\)

\(\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{5}-\frac{1}{6}\right)x10-X=0\)

\(\left(\frac{1}{1}-\frac{1}{6}\right)x10-X=10\)

\(\frac{5}{6}x10-X=0\)

\(X=\frac{5}{6}x10=\frac{25}{3}\)

Đúng nha !!!!

1/a/\(\frac{5}{7}\cdot4:\frac{5}{9}=\frac{20}{7}:\frac{5}{9}=\frac{20}{7}\cdot\frac{9}{5}=\frac{36}{7}\)

b/\(8\cdot\frac{2}{3}:\frac{1}{2}=\frac{16}{3}:\frac{1}{2}=\frac{16}{3}\cdot\frac{2}{1}=\frac{32}{3}\)

c/\(6:\frac{3}{5}-\frac{7}{6}\cdot\frac{6}{7}=6\cdot\frac{5}{3}-1=10-1=9\)

2/a/\(\frac{35}{9}:x=\frac{35}{6}\)

\(x=\frac{35}{9}:\frac{35}{6}=\frac{35}{9}\cdot\frac{6}{35}\)

\(x=\frac{2}{3}\)

b/\(\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}\right)\cdot10-x=0\)

\(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)\cdot10-x=0\)

\(\left(\frac{30}{60}+\frac{10}{60}+\frac{5}{60}+\frac{2}{30}\right)\cdot10-x=0\)

\(\frac{47}{60}\cdot10-x=0\)

\(\frac{47}{6}-x=0\)

\(x=\frac{47}{6}-0\)

\(x=\frac{47}{6}\)

xs

\(A=\frac{4^5.9^4-2.6^9}{2^{10}.3^8-6^8.20}\)

\(A=\frac{\left(2^2\right)^5.\left(3^2\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8-\left(2.3\right)^8.2^2.5}\)

\(A=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8-2^{10}.3^8.5}\)

\(A=\frac{2^{10}.\left(3^8-3^9\right)}{2^{10}.3^8.\left(1-5\right)}=\frac{3^8-3^9}{3^8.\left(-4\right)}=\frac{3^8.\left(1-3\right)}{3^8.\left(-4\right)}=\frac{-2}{-4}=\frac{1}{2}\)

Vậy A = \(\frac{1}{2}\)

\(B=\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)

\(B=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}\)

\(B=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\)

\(B=\frac{2^{19}.3^9+3^9.2^{18}.5}{2^{19}.3^9+2^{20}.3^{10}}\)

\(B=\frac{2^{18}.3^9.\left(2+5\right)}{2^{19}.3^9\left(1+2.3\right)}=\frac{7}{2.7}=\frac{1}{2}\)

Vậy B = \(\frac{1}{2}\)

Bài 1:

a)

\(A=\dfrac{-5}{6}\cdot\dfrac{3}{10}\\ =\dfrac{\left(-5\right)\cdot3}{6\cdot10}\\ =\dfrac{-1}{4}\)

b)

\(B=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{12}\\ =\dfrac{4}{12}-\dfrac{3}{12}+\dfrac{1}{12}\\ =\dfrac{4-3+1}{12}\\ =\dfrac{1}{6}\)

Bài 2:

\(A=\left(\dfrac{-1}{5}\right)\cdot\dfrac{15}{4}+\left|\dfrac{4}{5}-\dfrac{14}{5}\right|:\dfrac{8}{3}\\ =\left(\dfrac{-1}{5}\right)\cdot\dfrac{15}{4}+\left|\dfrac{-10}{5}\right|\cdot\dfrac{3}{8}\\ =\left(\dfrac{-1}{5}\right)\cdot\dfrac{15}{4}+2\cdot\dfrac{3}{8}\\ =\dfrac{-3}{4}+\dfrac{3}{4}\\ =0\)

\(B=\left(\dfrac{-1}{2}\right)^2:1\dfrac{3}{8}+25\%\cdot\dfrac{3}{11}\\ =\left(\dfrac{-1}{2}\right)^2:\dfrac{11}{8}+\dfrac{3}{4}\cdot\dfrac{3}{11}\\ =\dfrac{1}{4}\cdot\dfrac{8}{11}+\dfrac{3}{4}\cdot\dfrac{3}{11}\\ =\dfrac{8}{44}+\dfrac{9}{44}\\ =\dfrac{17}{44}\)

\(C=\dfrac{-8}{5}+0,6+\left|\dfrac{-1}{2}\right|+\dfrac{1}{2}\\ =\dfrac{-8}{5}+\dfrac{3}{5}+\dfrac{1}{2}+\dfrac{1}{2}\\ =\left(\dfrac{-8}{5}+\dfrac{3}{8}\right)+\left(\dfrac{1}{2}+\dfrac{1}{2}\right)\\ =\left(-1\right)+1\\ =0\)

\(D=\dfrac{-5}{9}\cdot\dfrac{2}{13}+\dfrac{-5}{9}:\dfrac{13}{11}+1\dfrac{5}{9}\\ =\dfrac{-5}{9}\cdot\dfrac{2}{13}+\dfrac{-5}{9}\cdot\dfrac{11}{13}+\dfrac{14}{9}\\ =\dfrac{-5}{9}\cdot\left(\dfrac{2}{13}+\dfrac{11}{13}\right)+\dfrac{14}{9}\\ =\dfrac{-5}{9}\cdot1+\dfrac{14}{9}\\ =\dfrac{-5}{9}+\dfrac{14}{9}\\ =1\)

Bài 3:

a)

\(\dfrac{x}{2}+\dfrac{3}{4}=\dfrac{1}{4}\\ \dfrac{x}{2}=\dfrac{1}{4}-\dfrac{3}{4}\\ \dfrac{x}{2}=\dfrac{-1}{2}\\ \Rightarrow x=-1\)

b)

\(\dfrac{3}{5}x+0,4x=2\\\dfrac{3}{5}x+\dfrac{2}{5}x=2\\ x\left(\dfrac{3}{5}+\dfrac{2}{5}\right)=2\\ x=2 \)

c)

\(\dfrac{x}{-3}=\dfrac{7}{6}+\left(\dfrac{-15}{18}\right)\\ \dfrac{-x}{3}=\dfrac{1}{3}\\ \Rightarrow-x=1\\ \Leftrightarrow x=-1\)

d)

\(\dfrac{4}{3}\cdot\left(\dfrac{1}{6}-\dfrac{1}{2}\right)< x< \dfrac{2}{3}\cdot\left(\dfrac{-1}{6}+\dfrac{3}{4}\right)\\ \Leftrightarrow\dfrac{4}{3}\cdot\dfrac{-1}{3}< x< \dfrac{2}{3}\cdot\dfrac{7}{12}\\ \Leftrightarrow\dfrac{-4}{9}< x< \dfrac{7}{18}\\ \Rightarrow x=0\)