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a) \(\frac{1}{10}-\frac{1}{40}-\frac{1}{88}-\frac{1}{154}-\frac{1}{238}-\frac{1}{340}\)
\(=\frac{1}{10}-\left(\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+\frac{1}{17.20}\right)\)
\(=\frac{1}{10}-\frac{1}{3}.\left(\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+\frac{3}{17.20}\right)\)
\(=\frac{1}{10}-\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\right)\)
\(=\frac{1}{10}-\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{20}\right)\)
\(=\frac{1}{10}-\frac{1}{3}.\frac{3}{20}\)
\(=\frac{1}{10}-\frac{1}{20}=\frac{2}{20}-\frac{1}{20}=\frac{1}{20}\)
Ta có : \(\left(\frac{1}{49}-\frac{1}{2^2}\right)\left(\frac{1}{49}-\frac{1}{3^2}\right)\left(\frac{1}{49}-\frac{1}{4^2}\right).......\left(\frac{1}{49}-\frac{1}{40^2}\right)\)
\(=\left(\frac{1}{49}-\frac{1}{2^2}\right)\left(\frac{1}{49}-\frac{1}{3^2}\right)......\left(\frac{1}{49}-\frac{1}{7^2}\right)......\left(\frac{1}{49}-\frac{1}{40^2}\right)\)
\(=\left(\frac{1}{49}-\frac{1}{2^2}\right)\left(\frac{1}{49}-\frac{1}{3^2}\right)......0......\left(\frac{1}{49}-\frac{1}{40^2}\right)\)
\(=0\)
\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{98.99.100}-3x=\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+...+\frac{1}{27.28.29.30}\)
\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{98.99}-\frac{1}{99.100}\right)-3x=\frac{1}{3}\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{27.28.29}-\frac{1}{28.29.30}\right)\)
\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{99.100}\right)-3x=\frac{1}{3}\left(\frac{1}{1.2.3}-\frac{1}{28.29.30}\right)\)
\(\Rightarrow\frac{4949}{19800}-3x=\frac{451}{8120}\)
\(\Rightarrow3x=\frac{4949}{19800}-\frac{451}{8120}\)
\(\Rightarrow x=\left(\frac{4949}{19800}-\frac{451}{8120}\right):3\)
e, \(\frac{3}{14}:\frac{1}{28}-\frac{13}{21}:\frac{1}{28}+\frac{28}{42}:\frac{1}{28}-8\)
\(=\left(\frac{3}{14}-\frac{13}{21}+\frac{2}{3}\right):\frac{1}{28}-8\)
\(=\frac{11}{42}:\frac{1}{28}-8\)
\(=\frac{22}{3}-8\)
\(=-\frac{2}{3}\)
e, \(\frac{3}{14}:\frac{1}{28}-\frac{13}{21}:\frac{1}{28}+\frac{28}{42}:\frac{1}{28}-8\)
\(=\left(\frac{3}{14}-\frac{13}{21}+\frac{2}{3}\right):\frac{1}{28}-8\)
\(=\frac{11}{42}:\frac{1}{28}-8\)
\(=\frac{22}{3}-8\)
\(=-\frac{2}{3}\)
Ta có: \(B=\frac{1}{112}-\frac{1}{84}-\frac{1}{60}-\frac{1}{40}-\frac{1}{24}-\frac{1}{12}-\frac{1}{4}\)
\(\Rightarrow2B=\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)
\(\Rightarrow2B=\frac{1}{56}-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)
\(\Rightarrow2B=\frac{1}{56}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)
\(\Rightarrow2B=\frac{1}{56}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(\Rightarrow2B=\frac{1}{56}-\left(1-\frac{1}{7}\right)\)
\(\Rightarrow2B=\frac{1}{56}-\frac{6}{7}\)
\(\Rightarrow2B=-\frac{47}{56}\)
\(\Rightarrow B=-\frac{47}{112}\)
Hok tốt nha^^
B. 1/3 - 1/3 - 3/5 +3/5 + 5/7 - 5/7 + 9/11 - 9/11 -11/13 + 11/ 13 + 7/9 + 13/15
= 0 -0-0-0-0+7/9 +13/15
= 74/45
Đặt A= \(\frac{1}{10}-\frac{1}{40}-..-\frac{1}{340}\)
A=\(\frac{1}{10}-\left(\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{17.20}\right)\)
3A= \(\frac{1}{10}-(\frac{3}{5.8}+...+\frac{3}{17.20})\)
3A=\(\frac{1}{10}-\left(\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\right)\)
3A=\(\frac{1}{10}-\left(\frac{1}{5}-\frac{1}{20}\right)\)
3A=\(\frac{1}{10}-\frac{3}{20}\)
3A=\(-\frac{1}{20}\)
A=\(-\frac{1}{60}\)
ttiikk nha bạn
\(=\frac{1}{2.5}-\frac{1}{5.8}-...-\frac{1}{17.20}.\)
\(=\frac{1}{10}-\frac{1}{3}\left(\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{17.20}\right).\)
\(=\frac{1}{10}-\frac{1}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\right).\)
\(=\frac{1}{10}-\frac{1}{3}\left(\frac{1}{5}-\frac{1}{20}\right)\)
\(=\frac{1}{10}-\frac{1}{3}.\frac{3}{20}\)
\(=\frac{1}{20}\)