a) 2 -1/9.10 -1/9.8 -1/8.7 - .......-1/3.2 -1/2.1 b) 5/2.8 +5/8.14 +5/20.26 +5/26.32 c) 15/3.10 +15/10.17 +15/17.24 +15/24.31 +15/31.38 giải chi tiết cho mình nha mình tick...
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a) 2 -1/9.10 -1/9.8 -1/8.7 - .......-1/3.2 -1/2.1 b) 5/2.8 +5/8.14 +5/20.26 +5/26.32 c) 15/3.10 +15/10.17 +15/17.24 +15/24.31 +15/31.38 giải chi tiết cho mình nha mình tick cho
a)\(2-\frac{1}{10.9}-\frac{1}{9.8}-\frac{1}{8.7}-.....-\frac{1}{3.2}-\frac{1}{2.1}=2-\left(\frac{1}{10.9}+\frac{1}{9.8}+\frac{1}{8.7}+....+\frac{1}{3.2}+\frac{1}{2.1}\right)\)
\(=2-\left(\frac{1}{10}-\frac{1}{9}+\frac{1}{9}-\frac{1}{8}+\frac{1}{8}-\frac{1}{7}+....+\frac{1}{3}-\frac{1}{2}+\frac{1}{2}-1\right)\)
\(=2-\left(\frac{1}{10}-1\right)=2-\frac{-9}{10}=\frac{29}{10}\)
b)\(\frac{5}{2.8}+\frac{5}{8.14}+\frac{5}{14.20}+\frac{5}{20.26}+\frac{5}{26.32}=5\left(\frac{1}{2.8}+\frac{1}{8.14}+\frac{1}{14.20}+\frac{1}{20.26}+\frac{1}{26.32}\right)\)
\(=5\left[\frac{1}{6}\left(\frac{1}{2}-\frac{1}{8}+\frac{1}{8}-\frac{1}{14}+\frac{1}{14}-\frac{1}{20}+\frac{1}{20}-\frac{1}{26}+\frac{1}{26}-\frac{1}{32}\right)\right]\)
\(=5\left[\frac{1}{6}\left(\frac{1}{2}-\frac{1}{32}\right)\right]=5\left(\frac{1}{6}.\frac{15}{32}\right)=5.\frac{5}{64}=\frac{25}{64}\)