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\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)
\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)
\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\frac{14}{15}\)
\(=\frac{7}{15}\)
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)\(\frac{1414+1515+...+1919}{2020+2121+...+2525}\)
\(\Rightarrow\frac{101\left(14+15+16+17+18+19\right)}{101\left(20+21+22+23+24+25\right)}\)
\(=\frac{14+15+16+17+18+19}{20+21+22+23+24+25}\)
\(=\frac{\left(19+14\right).6:2}{\left(25+20\right).6:2}=\frac{19+14}{25+20}=\frac{33}{45}=\frac{11}{15}\)
\(\frac{1414+1515+1616+1717+1818+1919}{2000+2121+2222+2323+2424+2525}\)
\(=\frac{101.\left(14+15+16+17+18+19\right)}{101.\left(20+21+22+23+24+25\right)}\)
\(\frac{14+15+16+17+18+19}{20+21+22+23+24+25}=\frac{99}{135}=\frac{11}{15}\)
L_I_K_E NHA
1414+1515+1616+1717+1818+1919/2020+2121+2222+2323+2424+2525=2525 nhé bạn
\(\frac{\text{(1414+1919)+(1515+1818)+(1616+1717) }}{\left(2020+2525\right)+\left(2121+2424\right)+\left(2222+2323\right)}\)\(=\frac{3333+3333+3333}{4545+4545+4545}=\frac{3333}{4545}=\frac{11}{15}\)
\(\frac{1414+1515+1616+1717+1818+1919}{2020+2121+2222+2323+2424+2525}\)
\(=\frac{101\times\left(14+15+16+17+18+19\right)}{101\times\left(20+21+22+23+24+25\right)}\)
\(=\frac{14+15+16+17+18+19}{20+21+22+23+24+25}\)
+) 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
\(\Leftrightarrow\frac{99}{135}=\frac{11}{15}\)
Lục Minh Hoàng cho mình hỏi tại sao lại có 1/2 vậy ?
1/3+1/15+1/35+1/63+1/99+1/143+1/195
=1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15
suy ra 2(1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15)
=2/1*3+2/3*5+2/5*7+2/7*9+2/9*11+2/11*13+2/13*15
=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15
=1-1/15
=14/15
a=14/15 chia 2=7/15