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1/4*5+1/5*6+1/6*7+1/7*8=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1/4-1/8
1/8
=\(\frac{2001x2004x1001x2006}{2004x2006x2001x2002}\)=\(\frac{1}{2}\)
\(=\frac{2001.2004.1001.2002}{2004.2006.2001.2002}=\frac{1.1.1001.1}{1.2006.1.1}=\frac{1001}{2006}\)
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
= \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)
= \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
= \(\frac{1}{2}-\frac{1}{7}\)
= \(\frac{5}{14}\)
a) \(\frac{55}{32}\)
b) \(\frac{90}{48}\)
c) \(\frac{76}{15}\)
d) \(\frac{552}{119}\)
\(\frac{9}{16}+\frac{37}{32}=\frac{18}{32}+\frac{37}{32}=\frac{55}{32}\)
\(\frac{126}{48}-\frac{12}{16}=\frac{21}{8}-\frac{6}{8}=\frac{15}{8}\)
\(\frac{19}{15}\times\frac{32}{8}=\frac{19}{15}\times4=\frac{76}{15}\)
\(\frac{23}{17}:\frac{7}{24}=\frac{23}{17}.\frac{24}{7}=4\frac{76}{119}\)
\(A=1+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{10.11}\)
\(=1+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)
\(=1+\frac{1}{2}-\frac{1}{11}=\frac{31}{22}\)
\(A=1+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{90}+\frac{1}{110}\)
\(A=1+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+...+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}\)
\(A=1+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(A=1+\frac{1}{2}-\frac{1}{11}\)
\(A=\frac{31}{22}\)
Vậy \(A=\frac{31}{22}\)
\(\frac{1}{3}+\frac{1}{9}+\frac{1}{18}+\frac{1}{30}+..+\frac{1}{135}\)
\(=\frac{1}{3}+\frac{1}{9}+\frac{1}{18}+\frac{1}{30}+\frac{1}{45}+\frac{1}{63}+\frac{1}{84}+\frac{1}{108}+\frac{1}{135}\)
\(=\frac{1}{1\times3}+\frac{1}{3\times3}+\frac{1}{3\times6}+\frac{1}{6\times5}+\frac{1}{5\times9}+\frac{1}{9\times7}+\frac{1}{7\times12}+\frac{1}{12\times9}+\frac{1}{9\times15}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{9}+\frac{1}{9}-\frac{1}{15}\)
( gạch bỏ các phân số giống nhau )
\(=1-\frac{1}{15}\)
\(=\frac{14}{15}\)
CHÚC BẠN HỌC TỐT!!!!!
\(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
\(=\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\)
\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
\(=\frac{1}{4}-\frac{1}{7}\)
\(=\frac{7}{28}-\frac{4}{28}\)
\(=\frac{3}{28}\)
Chúc bạn học tốt
Ta có :
\(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
\(=\)\(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)
\(=\)\(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
\(=\)\(\frac{1}{4}-\frac{1}{7}\)
\(=\)\(\frac{3}{28}\)
Chúc bạn học tốt ~