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\(A=\frac{2}{3}+\frac{2}{15}+...+\frac{2}{143}\)
\(A=\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{11\cdot13}\)
\(A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\)
\(A=1-\frac{1}{13}=\frac{12}{13}\)
\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\)
\(=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\)
\(=1-\frac{1}{13}\)
\(=\frac{12}{13}\)
1/3 + 1/15 + 1/35+ 1/63 +...... + 1/195
= 1/3 + 1/3x5 + 1/5 x7 + 1/7x9 + ....+1/13x15
= 1/3+1/3-1/5+1/5-1/7+1/7-1/9+....+1/13-1/15 ( vì +- nên rút gọn )
= 1/3+1/3-1/15
=3/5
=1/1.3+1/3.5+1/5.7+...+1/13.15
=1/2.2(1/1.3+1/3.5+1/5.7+...+1/13.15)
=1/2(2/1.3+2/3.5+2/5.7+...+2/13.15)
=1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/13-1/15)
=1/2[(1-1/15)+(1/3-1/3)+(1/5-1/5)+...+(1/13-1/15)]
=1/2[(1-1/15)+0+...+0=1/2(1-1/15)=1/2.14/15=14/30=7/15
=[2/3+2/99]+[2/35+2/63]+2/15
=24/99+[4/45+2/15]
=24/99+2/9
=46/99
\(=\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}\)
\(=\frac{1}{2}\times\left(\frac{2}{1}-\frac{2}{3}+\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+\frac{2}{7}-\frac{2}{9}+\frac{2}{9}-\frac{2}{11}\right)\)
\(=\frac{1}{2}\times\frac{20}{11}=\frac{10}{11}\)
\(\frac{16}{3}:\frac{8}{3}=\frac{16}{3}\times\frac{3}{8}=\frac{16}{8}=2\)
\(\frac{63}{35}:\frac{21}{5}=\frac{63}{35}.\frac{5}{21}=\frac{3}{7}.\frac{1}{1}=\frac{3}{7}\)
\(\frac{8}{14}\times\frac{7}{8}=\frac{7}{14}=\frac{1}{2}\)
\(\frac{19}{14}\times\frac{7}{15}=\frac{19}{2}\times\frac{1}{15}=\frac{19}{30}\)
\(a,\frac{16}{3}:\frac{8}{3}=\frac{16}{3}\times\frac{3}{8}=\frac{8\times2\times3}{3\times8}=2\)
\(b,\frac{63}{35}:\frac{21}{5}=\frac{63}{35}\times\frac{5}{21}=\frac{21\times3\times5}{5\times7\times21}=\frac{3}{7}\)
\(c,\frac{8}{14}\times\frac{7}{8}=\frac{8\times7}{7\times2\times8}=\frac{1}{2}\)
\(d,\frac{19}{14}\times\frac{7}{15}=\frac{19\times7}{7\times2\times15}=\frac{19}{30}\)
Học tốt
\(a,\frac{5\cdot84\cdot105}{35\cdot50\cdot21}=\frac{1\cdot4\cdot3}{1\cdot10\cdot1}=\frac{1\cdot2\cdot3}{1\cdot5\cdot1}=\frac{6}{5}\)
\(b,\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{8}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{7}{8}\)
\(=\frac{1}{8}\)
a)
\(\frac{5\cdot84\cdot105}{35\cdot50\cdot21}\)
\(=\frac{5\cdot7\cdot2\cdot6\cdot35\cdot3}{35\cdot5\cdot10\cdot3\cdot7}\)
\(=\frac{6}{5}\)
Viết 1 phân số vào dãy sau: \(\frac{1}{3};\frac{1}{15};\frac{1}{35};\frac{1}{63};...\)
Giúp mình với!
\(\frac{1}{3};\frac{1}{15};\frac{1}{35};\frac{1}{63}\)
Phân tích : \(\frac{1}{3}=\frac{1}{1\cdot3};\frac{1}{15}=\frac{1}{3\cdot5};\frac{1}{35}=\frac{1}{5\cdot7};\frac{1}{63}=\frac{1}{7\cdot9}\)
\(\Leftrightarrow n=\frac{1}{9\cdot11}=\frac{1}{99}\)