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18 x \(\left(\frac{1919}{2121}+\frac{888}{999}\right)\)
= 18 x \(\frac{113}{63}\)
= \(\frac{226}{7}\)
a ) \(\frac{1919}{2121}=\frac{19.101}{21.101}=\frac{19}{21}\)
b) \(\frac{191191}{212212}=\frac{191.1001}{212.1001}=\frac{191}{212}\)
\(\frac{1414+1515+1616+1717+1818+1919}{2020+2121+2222+2323+2424+2525}\)
\(=\frac{101\times\left(14+15+16+17+18+19\right)}{101\times\left(20+21+22+23+24+25\right)}\)
\(=\frac{14+15+16+17+18+19}{20+21+22+23+24+25}\)
+) Tử số :
Số các số hạng là : ( 19 - 14 ) : 1 + 1 = 6 ( số )
Tổng là : ( 19 + 14 ) x 6 : 2 = 99
+) Mẫu số :
Số các số hạng là : ( 25 - 20 ) : 1 + 1 = 6 ( số )
Tổng là : ( 25 + 20 ) x 6 : 2 = 135
\(\Leftrightarrow\frac{99}{135}=\frac{11}{15}\)
\(\frac{1414+1515+1616+1717+1818+1919}{2020+2121+2222+2323+2424+2525}\)
= \(\frac{\left(1414+1919\right)+\left(1515+1818\right)+\left(1616+1717\right)}{\left(2020+2525\right)+\left(2121+2424\right)+\left(2222+2323\right)}\)
= \(\frac{3333+3333+3333}{4545+4545+4545}=\frac{3333}{4545}=\frac{11}{15}\)
t i c k nhé!! 45435436457
\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)
\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)
\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\frac{14}{15}\)
\(=\frac{7}{15}\)
a) \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)
\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{15}\right)=\frac{1}{2}.\frac{14}{15}\)\(=\frac{7}{15}\)
b)\(\frac{1414+1515+...+1919}{2020+2121+...+2525}\)
\(\Rightarrow\frac{101\left(14+15+16+17+18+19\right)}{101\left(20+21+22+23+24+25\right)}\)
\(=\frac{14+15+16+17+18+19}{20+21+22+23+24+25}\)
\(=\frac{\left(19+14\right).6:2}{\left(25+20\right).6:2}=\frac{19+14}{25+20}=\frac{33}{45}=\frac{11}{15}\)
đặt A=1919/2121=1919:101/2121:101=19/21
B=191919/212121=191919:10101/212121:10101=19/21
=>A=B=19/21
\(18.\frac{113}{63}\)
\(=\frac{226}{7}\)
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