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\(\dfrac{55}{11}\cdot6+\dfrac{55}{16}\cdot21+\dfrac{55}{21}\cdot26+\dfrac{55}{26}\cdot31+\dfrac{55}{31}\cdot36+\dfrac{55}{36}\cdot41=30+\dfrac{1155}{16}+\dfrac{1430}{21}+\dfrac{1705}{26}+\dfrac{1980}{31}+\dfrac{2255}{36}=\dfrac{12186720}{406224}+\dfrac{29324295}{406224}+\dfrac{27661920}{406224}+\dfrac{26638920}{406224}+\dfrac{25945920}{406224}+\dfrac{25445420}{406224}=\dfrac{147203195}{406224}\)
a) \(S4=\frac{3}{50}+\frac{3}{150}+\frac{3}{300}+...+\frac{3}{9500}\)
\(S4=\frac{3}{5.10}+\frac{3}{10.15}+\frac{3}{15.20}+...+\frac{3}{95.100}\)
\(S4=\frac{3}{5}\left(\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+\frac{1}{15}-\frac{1}{20}+...+\frac{1}{95}-\frac{1}{100}\right)\)
\(S4=\frac{3}{5}\left(\frac{1}{5}-\frac{1}{100}\right)\)
\(S4=\frac{3}{5}.\frac{19}{100}\)
\(S4=\frac{57}{500}\Rightarrow S=\frac{57}{500}:4=\frac{57}{2000}\)
b) \(S5=\frac{55}{11.16}+\frac{55}{16.21}+...+\frac{55}{36.41}\)
\(S5=\frac{55}{5}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{36}-\frac{1}{41}\right)\)
\(S5=11.\left(\frac{1}{11}-\frac{1}{41}\right)\)
\(S5=11.\frac{30}{451}\)
\(S5=\frac{30}{41}\Rightarrow S=\frac{30}{41}:5=\frac{6}{41}\)
1) 2155-(174+2155)+(-68+174-7)-1911-(1234-1911)
=2155-174-2155+(-68)+174-7-1911-1234+1911
=(2155-2155)+(174-174)+(1911-1911)-(68+7+1234)
= 0 + 0 + 0 - 1309
= -1309
a) \(\dfrac{-5}{9}-\dfrac{4}{15}+\dfrac{2}{9}-\dfrac{11}{15}\)
\(=\left(\dfrac{-5}{9}+\dfrac{2}{9}\right)-\left(\dfrac{4}{15}+\dfrac{11}{15}\right)\)
\(=\dfrac{-3}{9}-\dfrac{15}{15}\)
\(=-\dfrac{1}{3}-1\)
\(=-\dfrac{4}{3}\)
b) \(\dfrac{-8}{13}-\dfrac{7}{16}+\dfrac{21}{13}-\dfrac{1}{6}\)
\(=\left(\dfrac{-8}{13}+\dfrac{21}{13}\right)-\dfrac{7}{16}-\dfrac{1}{6}\)
\(=\dfrac{13}{13}-\dfrac{29}{48}\)
\(=1-\dfrac{29}{48}\)
\(=\dfrac{19}{48}\)
c) \(\dfrac{-15}{25}-\dfrac{14}{21}+\dfrac{8}{5}-\dfrac{5}{3}\)
\(=\dfrac{-3}{5}-\dfrac{2}{3}+\dfrac{8}{5}-\dfrac{5}{3}\)
\(=\left(\dfrac{-3}{5}+\dfrac{8}{5}\right)-\left(\dfrac{2}{3}+\dfrac{5}{3}\right)\)
\(=\dfrac{5}{5}-\dfrac{7}{3}\)
\(=1-\dfrac{7}{3}\)
\(=-\dfrac{4}{3}\)
a: =-5/9+2/9-11/15-4/15
=-3/9-1
=-12/9=-4/3
b: =-8/13+21/13-7/16-1/6
=1-1/6-7/16
=5/6-7/16
=19/48
c: =-15/25+8/5-2/3-5/3
=-7/3+1
=-4/3
1: Ta có: \(2155-\left(174+2155\right)+\left(-68+174\right)\)
\(=2155-174-2155-68+174\)
=-68
2) Ta có: \(-25\cdot72+25\cdot21-49\cdot25\)
\(=-25\cdot\left(72-21+49\right)\)
\(=-25\cdot100=-2500\)
1) 2155-(174+2155)+(-68+174)
=2155-174-2155-68+174
=2155-2155+174-174-68
=0+0-68
=-68
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