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\(1+2+...+n=\frac{n\left(n+1\right)}{2}\)
\(\Rightarrow E=1+\frac{1}{2}\frac{2.3}{2}+\frac{1}{3}.\frac{3.4}{2}+\frac{1}{4}.\frac{4.5}{2}+...+\frac{1}{200}.\frac{200.201}{2}\)
\(=1+\frac{1}{2}\left(3+4+5+...+201\right)\)
\(=1+\frac{1}{2}\left(1+2+3+...+201-1-2\right)\)
\(=1+\frac{1}{2}\left(\frac{201.202}{2}-3\right)=10150\)
\(\frac{21}{5}\left|x\right|< 2019\Rightarrow\left|x\right|< 2019\div\frac{21}{5}=\frac{3365}{7}\)
\(\Rightarrow-480\le x\le480\)
\(\Rightarrow\sum x=-480+480-479+479+...+-1+1+0=0\)
\(\frac{2^{24}\left(x-3\right)}{\frac{81}{35}.\left(6.2^{24}-2^{26}\right)}=\frac{25}{9}\)
\(\Leftrightarrow\frac{2^{24}\left(x-3\right)}{2^{24}\left(6-2^2\right)}=\frac{25}{9}.\frac{81}{35}\)
\(\Leftrightarrow\frac{x-3}{2}=\frac{45}{7}\)
\(\Leftrightarrow x-3=\frac{90}{7}\)
\(\Rightarrow x=\frac{111}{7}\)
Bài 1 : Tính :
a, \(-\frac{8}{3}.\frac{6}{13}.\frac{7}{13}.\frac{-3}{8}+1\frac{3}{8}\)
\(=\left(-\frac{8}{3}.-\frac{3}{8}\right).\left(\frac{6}{13}.\frac{7}{13}\right)+1\frac{3}{8}\)
\(=1.\frac{42}{169}+1\frac{3}{8}\)
\(=\frac{2195}{1352}\)
b) \(75\%-\left(\frac{5}{2}+\frac{5}{3}\right)+\left(-\frac{1}{2}\right)^2\)
\(=\frac{3}{4}-\frac{25}{6}+\frac{1}{4}\)
\(=\frac{3}{4}+\frac{1}{4}-\frac{25}{6}\)
\(=1-\frac{25}{6}\)
\(=-\frac{19}{6}\)
~Hok tốt~
Bài 2 :
a)\(\frac{3}{5}.x-\frac{2}{3}=\frac{1}{2}\) b) \(\left(\frac{1}{2}-x\right).\frac{2}{3}=\frac{1}{8}\)
\(\frac{3}{5}.x=\frac{1}{2}+\frac{2}{3}\) \(\frac{1}{2}-x=\frac{1}{8}:\frac{2}{3}\)
\(\frac{3}{5}.x=\frac{7}{6}\) \(\frac{1}{2}-x=\frac{3}{16}\)
\(x=\frac{7}{6}:\frac{3}{5}\) \(x=\frac{1}{2}-\frac{3}{16}\)
\(x=\frac{35}{18}\) \(x=\frac{5}{16}\)
c) \(\left|2x-\frac{3}{7}\right|-\frac{1}{2}=\frac{3}{4}\)
\(\left|2x-\frac{3}{7}\right|=\frac{3}{4}+\frac{1}{2}\)
\(\left|2x-\frac{3}{7}\right|=\frac{5}{4}\)
\(\Rightarrow2x-\frac{3}{7}\in\left\{\frac{5}{4};-\frac{5}{4}\right\}\)
\(TH1:2x-\frac{3}{7}=\frac{5}{4}\) \(TH2:2x-\frac{3}{7}=-\frac{5}{4}\)
\(\Rightarrow2x=\frac{5}{4}+\frac{3}{7}\) \(\Rightarrow2x=-\frac{5}{4}+\frac{3}{7}\)
\(2x=\frac{47}{28}\) \(2x=-\frac{23}{28}\)
\(x=\frac{47}{28}:2\) \(2x=-\frac{23}{28}:2\)
\(x=\frac{47}{56}\) \(2x=-\frac{23}{56}\)
\(\Rightarrow x\in\left\{\frac{47}{56};-\frac{23}{56}\right\}\)
\(2\left(\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{1}{9}\)
\(\Leftrightarrow2\left(\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{1}{9}\)
\(\Leftrightarrow2\left(\frac{1}{9}-\frac{1}{x+1}\right)=\frac{1}{9}\)
\(\Leftrightarrow\frac{1}{9}-\frac{1}{x+1}=\frac{1}{9}\div2\)
\(\Leftrightarrow\frac{1}{9}-\frac{1}{x+1}=\frac{1}{18}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{9}-\frac{1}{18}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{18}\)
\(\Leftrightarrow x+1=18\)
\(\Leftrightarrow x=18-1\)
\(\Leftrightarrow x=17\)
\(\left|x\right|-\frac{3}{4}=\frac{5}{3}\)
\(\Leftrightarrow\left|x\right|=\frac{5}{3}+\frac{3}{4}\)
\(\Leftrightarrow\left|x\right|=\frac{20}{12}+\frac{9}{12}\)
\(\Leftrightarrow\left|x\right|=\frac{29}{12}\)
\(\Leftrightarrow x=\pm\frac{29}{12}\)
Bài 1:
1) \(\frac{11}{3}\): 3\(\frac{1}{3}\)- 3
= \(\frac{11}{3}\): \(\frac{10}{3}\)- 3
= \(\frac{11}{3}\). \(\frac{3}{10}\)- 3
= \(\frac{11}{10}\)- 3
= \(\frac{-19}{10}\)
2) \(\frac{5}{6}\): \(\frac{3}{52}\) - \(\frac{5}{6}\). 47\(\frac{1}{3}\)
= \(\frac{5}{6}\) . \(\frac{52}{3}\)- \(\frac{5}{6}\). 47\(\frac{1}{3}\)
= \(\frac{5}{6}\).(\(\frac{52}{3}\)- 47\(\frac{1}{3}\))
= \(\frac{5}{6}\).( -30)
= -25
Ngày xưa mình thi đề còn dễ hơn đề của bạn
Mình đưa cái đề này cho bọn ĐT toán lớp mình làm mà chúng nó còn chả làm được 
Phùng Tuệ Minh hóng lắm mới đến ngày đc khôi phục, đưa lên CHH jup t đi tuy hơi muộn màng =)