Ta có:   \(M=\frac{4}{1.2.3}+\frac{4}{2.3.4}+...+\frac{4}{8.9.10}\)

             \(M=4\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right)\)

             \(M=4.\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)\)

             \(M=2\left(\frac{1}{2}-\frac{1}{90}\right)=1-\frac{1}{45}=\frac{44}{45}\)

Vậy \(M=\frac{44}{45}\)

\(M=\frac{4}{1.2.3}+\frac{4}{2.3.4}+...+\frac{4}{8.9.10}\)

\(=2.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{8.9.10}\right)\)

\(=2.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)\)

\(=2.\left(\frac{1}{1.2}-\frac{1}{9.10}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{90}\right)\)

\(=2.\frac{22}{45}\)

\(=\frac{44}{45}\)

Cho hỏi chút, ngày mai giải còn kịp không =))) ? Nếu có người giải trước rồi thì thôi, cũng không chắc giải full được mấy :/

Được nha bạn nameless, thứ tư mình mới phải nộp thầy.

\(\frac{1}{9.10}\)có x k bn?

k có x như trên đề thì hơi vl đấy.

phiền bn xem lại.

\(\frac{1}{1\cdot2}\times+\cdot\cdot\cdot+\frac{1}{9\cdot10}\times=\frac{18}{5}\)

\(\Rightarrow\left(\frac{1}{1\cdot2}+\cdot\cdot\cdot+\frac{1}{9\cdot10}\right)\times=\frac{18}{5}\)

\(\Rightarrow\left(1-\frac{1}{2}+\cdot\cdot\cdot+\frac{1}{9}-\frac{1}{10}\right)\times=\frac{18}{5}\)

\(\Rightarrow\left(1-\frac{1}{10}\right)\times=\frac{18}{5}\)

\(\Rightarrow\frac{9}{10}\times=\frac{18}{5}\)

\(\Rightarrow\times=\frac{18}{5}:\frac{9}{10}\)

\(\Rightarrow\times=4\)

a) \(4.5^2-81:3^2=4.25-81:9=100-9=91\)

b) \(3^3.23-3^3.19=3^3.\left(23-19\right)=27.4=108\)

c) \(2^4.5-[131-\left(13-4\right)^2]=16.5-\left(131-9^2\right)=80-\left(131-81\right)=80-50=30\)

d) \(100:\left\{250:\left[450-\left(4.5^3-2^2.25\right)\right]\right\}\)

\(=100:\left\{250:\left[450-4.\left(125-25\right)\right]\right\}\)

\(=100:\left[250:\left(450-4.100\right)\right]\)

\(=100:\left[250:\left(450-400\right)\right]=100:\left(250:50\right)=100:5=20\)

\(\frac{1}{2}\times+\frac{1}{4}\times+\frac{1}{8}\times=\frac{1}{16}\)

\(\Rightarrow\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\right)\times=\frac{1}{16}\)

\(\Rightarrow\frac{7}{8}\times=\frac{1}{16}\)

\(\Rightarrow\times=\frac{1}{14}\)

\(\frac{1}{2}x+\frac{1}{4}x+\frac{1}{8}x=\frac{1}{16}\)

\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\right)x=\frac{1}{16}\)

\(\frac{7}{8}x=\frac{1}{16}\)

\(x=\frac{1}{16}\div\frac{7}{8}\)

\(x=\frac{1}{14}\)

Tìm dãy số?

\(\left(2013.2014+2014.2015+2015.2016\right).\left(1+\frac{1}{3}-1-\frac{1}{3}\right)\)

\(=\left(2013.2014+2014.2015+2015.2016\right).0\)

= 0

\(\left|-1\frac{1}{2}\right|+25\%+\frac{1}{4}\)

\(=\left|-\frac{3}{2}\right|+\frac{1}{4}+\frac{1}{4}\)

\(=\frac{3}{2}+\frac{1}{2}\)

\(=2\)

a)369,693,963                       b)690,369,960,963,693