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\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2020}\)\(-\dfrac{1}{2022}\)
\(=1-\dfrac{1}{2022}\)
\(=\dfrac{2021}{2022}\)
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6F=1.3(5-1)+3.5(7-1)+5.7(9-3)+...99.101(103-97)
6F=1.3+1.3.5-1.3.5+3.5.7-3.5.7+.....-97.99.101+99.101.103
6F=3+99.101.103
6F=3+1029897
6F=1029900
F =1029900:6
F=171650
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Uk bạn ! Đây là toán bồi dưỡng học sinh giỏi toán 6 ! Giúp mik với ~ !
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\(B=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+..+\frac{1}{55}\)
\(B=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{110}\)
\(B=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{10.11}\)
\(B=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\right)\)
\(B=2.\left(\frac{1}{2}-\frac{1}{11}\right)=2.\frac{9}{22}=\frac{9}{11}\)