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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
a/ \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}+\frac{1}{1024}\)
= \(\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{8}\right)+...+\left(\frac{1}{256}-\frac{1}{512}\right)+\left(\frac{1}{512}-\frac{1}{1024}\right)\)
= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{256}-\frac{1}{512}+\frac{1}{512}-\frac{1}{1024}\)
= \(1-\frac{1}{1024}\)
= \(\frac{1023}{1024}\)
b/ \(\frac{1}{8}+\frac{1}{48}+\frac{1}{80}+...+\frac{1}{10200}\)
= \(\frac{1}{8}+\frac{1}{6\times8}+\frac{1}{8\times10}+...+\frac{1}{100\times102}\)
= \(\frac{1}{8}+\frac{1}{2}\times\left(\frac{2}{6\times8}+\frac{2}{8\times10}+...+\frac{2}{100\times102}\right)\)
= \(\frac{1}{8}+\frac{1}{2}\times\left(\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+...+\frac{1}{100}-\frac{1}{102}\right)\)
= \(\frac{1}{8}+\frac{1}{2}\times\left(\frac{1}{6}-\frac{1}{102}\right)\)
= \(\frac{1}{8}+\frac{1}{2}\times\frac{8}{51}\)
= \(\frac{1}{8}+\frac{4}{51}\)
= \(\frac{83}{408}\)
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 : \(\frac{1}{3}=\frac{1}{1\cdot3};\frac{1}{15}=\frac{1}{3\cdot5};\frac{1}{35}=\frac{1}{5\cdot7};\frac{1}{63}=\frac{1}{7\cdot9}\)
\(\Leftrightarrow n=\frac{1}{9\cdot11}=\frac{1}{99}\)
\(\frac{1}{3}\)+ \(\frac{1}{6}\)+ \(\frac{1}{12}\)+\(\frac{1}{24}\)+\(\frac{1}{48}\)+\(\frac{1}{96}\)
= ( \(\frac{1}{3}\)+\(\frac{1}{6}\)) + ( \(\frac{1}{12}\)+ \(\frac{1}{24}\)) + ( \(\frac{1}{48}\)+\(\frac{1}{96}\))
= \(\frac{1}{2}\) + \(\frac{1}{8}\) + \(\frac{1}{32}\)
= \(\frac{5}{8}\) + \(\frac{1}{32}\)
= \(\frac{21}{32}\)
1/100