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Ta có 1/1.2-1/2.3=2/1.2.3;1/2.3-1/3.4=2/2.3.4 .....1/98.99-1/99.100=2/98.99.100 2A=2/1.2.3+2/2.3.4+....+2/98.99.100 = 1/1.2-1/2.3+1/2.3-1/3.4+...+1/98.99-1/99.100 = 1/2-1/99.100 = 4949/9900 A =4949/19800
Đặt \(A=\frac{1}{1.3}+\frac{1}{2.4}+\frac{1}{3.5}+...+\frac{1}{97.99}+\frac{1}{99.100}\)
\(\Rightarrow2A=2\left(\frac{1}{1.3}+\frac{1}{2.4}+\frac{1}{3.5}+...+\frac{1}{97.99}+\frac{1}{98.100}\right)\)
\(\Rightarrow2A=\frac{2}{1.3}+\frac{2}{2.4}+\frac{2}{3.5}+...+\frac{2}{97.99}+\frac{2}{98.100}\)
\(\Rightarrow2A=\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{97.99}\right)+\left(\frac{2}{2.4}+\frac{1}{4.6}+...+\frac{1}{98.100}\right)\)
\(\Rightarrow2A=\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{97}-\frac{1}{99}\right)+\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\right)\)
\(\Rightarrow2A=\left(1-\frac{1}{99}\right)+\left(\frac{1}{2}-\frac{1}{100}\right)\)
\(\Rightarrow2A=\left(\frac{99}{99}-\frac{1}{99}\right)+\left(\frac{50}{100}-\frac{1}{100}\right)\)
\(\Rightarrow2A=\frac{98}{99}+\frac{49}{100}=\frac{9800}{9900}+\frac{4851}{9900}=\frac{14651}{9900}\)
\(\Rightarrow A=\frac{14651}{9900}:2=\frac{14651}{9900}.\frac{1}{2}=\frac{14651}{19800}\)
bạn nhớ thử lại nhé :)
2Q = 1-1/3-1/2+1/4+1/3-1/5-1/4+1/6-........+1/97-1/99-1/98+1/100 = 1-1/2-1/99+1/100 = 4949/9900 >> Q = 49499/19800
\(Q=\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+...+\frac{1}{97.99}-\frac{1}{98.100}\)
\(=\frac{1}{2}\left(1-\frac{1}{3}-\frac{1}{2}+\frac{1}{4}+\frac{1}{3}+\frac{1}{5}-\frac{1}{4}+\frac{1}{6}+...+\frac{1}{97}-\frac{1}{99}-\frac{1}{98}+\frac{1}{100}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{100}\right)=\frac{1}{2}.\frac{99}{100}=\frac{99}{200}\) (không chắc cho lắm :v)
\(M=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{37.38.39}=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+..+\frac{1}{37.38}-\frac{1}{38.39}\)
\(=\frac{1}{1.2}-\frac{1}{38.39}=\frac{1}{1}-\frac{1}{2}-\frac{1}{38}+\frac{1}{39}=\frac{370}{741}\)
X=2 nhé bạn.....đúng đó, vòng 12 mk 300 mà cx gặp câu này!!! Tick nha
