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Sao bn học nhanh thế mới có mấy tuần học mà đã học toán chứng minh rồi thế!
Cố lên nha bn !
Chúc bn có câu trả lời thoả đáng để giải bài toán này nha!
Chúc bn mãi mãi học giỏi!
Uk, mk cảm ơn bn đã chúc mk học giỏi.
Nhưng mk đã học tới toán chứng minh vì mk học nâng cao, giỏi hơn bn nhiều! OK?
Trả lời thì trả lời đừng ở đó mà ns nhiều!
*)\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)
=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
=\(1-\frac{1}{6}\)
=\(\frac{6}{6}-\frac{1}{6}\)
\(=\frac{5}{6}\)
*)\(\frac{2003}{1.2}+\frac{2003}{2.3}+\frac{2003}{3.4}+...+\frac{2003}{2002.2003}\)
\(=\frac{2003}{1}-\frac{2003}{2}+\frac{2003}{2}-\frac{2003}{3}+\frac{2003}{3}-\frac{2003}{4}+...+\frac{2003}{2002}-\frac{2003}{2003}\)
\(=2003-1\)
\(=2002\)
1) \(\frac{2}{5}\cdot\frac{1}{2}+\frac{1}{3}=\frac{1}{5}+\frac{1}{3}=\frac{8}{15}\)
2)\(\left(\frac{5}{7}-\frac{2}{5}\right):\frac{11}{7}=\frac{5}{7}:\frac{11}{7}-\frac{2}{5}:\frac{11}{7}=\frac{5}{7}\cdot\frac{7}{11}-\frac{2}{5}\cdot\frac{7}{11}=\frac{5}{11}-\frac{14}{55}=\frac{1}{5}\)
3)\(\frac{1-\frac{2}{3}+\frac{1}{4}}{2-\frac{1}{3}+\frac{1}{6}}=\frac{12-8+3}{12}:\frac{12-2+1}{6}=\frac{7}{12}\cdot\frac{\frac{6}{11}7}{22}\)
\(\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{8.9}+\frac{1}{9.10}\right)\times100-\left[\frac{5}{2}:\left(x+\frac{206}{100}\right)\right]:\frac{1}{2}=89\)
\(\Rightarrow\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\times100-\left[\frac{5}{2}:\left(x+\frac{206}{100}\right)\right]=\frac{89}{2}\)
\(\Rightarrow\left(1-\frac{1}{10}\right)\times100-\left[\frac{5}{2}:\left(x+\frac{206}{100}\right)\right]=\frac{89}{2}\)
\(\left(6+\left(\frac{1}{2}\right)^3-\left|-\frac{1}{2}\right|\right):\frac{3}{12}\)
\(=\left(6+\frac{1}{8}+\frac{1}{2}\right):\frac{1}{4}\)
=\(\frac{53}{8}:\frac{1}{4}\)
\(=\frac{53}{2}\)
a)30/60,-40/60,45/60,48/60
45/60>30/60>-40/60>-48/60
=3/4>1/2>-2/3>-4/5
a) \(\frac{x-3}{3}-1=\frac{x}{-4}\)
\(\Leftrightarrow\frac{x-3}{3}-\frac{3}{3}=\frac{x}{-4}\)
\(\Leftrightarrow\frac{x-6}{3}=\frac{x}{-4}\)
\(\Leftrightarrow-4\left(x-6\right)=3x\)
\(\Leftrightarrow-4x+24=3x\)
\(\Leftrightarrow24=3x+4x\)
\(\Leftrightarrow7x=24\)
\(\Leftrightarrow x=\frac{24}{7}\)
b) \(\frac{5}{8}-\left(x-\frac{1}{2}\right)=\frac{-3}{4}\)
\(\Leftrightarrow\frac{5}{8}-x+\frac{1}{2}=\frac{-3}{4}\)
\(\Leftrightarrow\frac{5}{8}+\frac{4}{8}-x=\frac{-3}{4}\)
\(\Leftrightarrow\frac{9}{8}-x=\frac{-3}{4}\)
\(\Leftrightarrow x=\frac{9}{8}+\frac{3}{4}\)
\(\Leftrightarrow x=\frac{15}{8}\)
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{2}{5}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2}{5}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2}{5}\)
\(\frac{1}{x+1}=\frac{1}{2}-\frac{2}{5}\)
\(\frac{1}{x+1}=\frac{1}{10}\)
\(\Rightarrow x+1=10\)
\(\text{Vậy x = 9}\)
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}=\frac{2}{5}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2}{5}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2}{5}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2}{5}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{10}\)
\(\Rightarrow x+1=10\)
\(\Rightarrow x=10-1\)
\(\Rightarrow x=9\)
Vẫy = 9
Tìm x biết:
\(\frac{x}{3}-\frac{3}{4}=\frac{1}{12}\)
\(\frac{x}{3}=\frac{1}{12}+\frac{3}{4}\)
\(\frac{x}{3}=\frac{5}{6}\)
\(x=\frac{5}{6}.3\)
\(x=\frac{5}{2}\)
Vậy \(x=\frac{5}{2}\)
\(\frac{29}{30}-\left(\frac{13}{23}+x\right)=\frac{7}{69}\)
\(\frac{13}{23}+x=\frac{29}{30}-\frac{7}{69}\)
\(\frac{13}{23}+x=\frac{199}{230}\)
\(x=\frac{199}{230}-\frac{13}{23}\)
\(x=\frac{3}{10}\)
Vậy \(x=\frac{3}{10}\)
Bài 2: tính
\(\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}\)
\(=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}\)
\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(=\frac{1}{5}-\frac{1}{11}\)
\(=\frac{6}{55}\)
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=\frac{1}{1}-\frac{1}{50}\)
\(=\frac{49}{50}\)
Bài 2:
1/30+1/42+1/56+1/72+1/90+1/110
=1/5.6+1/6.7+1/7.8+1/8.9+1/9.10+1/10.11
=1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11
=1/5-1/11=6/55
b)1/1.2+1/2.3+...+1/49.50
=1-1/2+1/2-1/3+...+1/49-1/50
=1-1/50
=49/50
\(19\frac{1}{4}+\frac{1}{2}.2\frac{1}{3}+5,75-\frac{1}{6}+74\)
=\(\frac{77}{4}+\frac{1}{2}.\frac{7}{3}+\frac{575}{100}-\frac{1}{6}+74\)
= \(\frac{77}{4}+\frac{7}{6}+\frac{23}{4}-\frac{1}{6}+74\)
= \(\left(\frac{77}{4}+\frac{23}{4}\right)+\left(\frac{7}{6}-\frac{1}{6}\right)+74\)
= \(\frac{100}{4}+1+74\)
= 100
^^
Đáp án là 100