Câu 2
a: 1/2+1/4+1/8+1/16+1/32+1/32
=3/8+1/8+1/16+1/16
=4/8+1/2=1
b: =1/50-1/51+1/51-1/52+...+1/99-1/100
=1/50-1/100=1/100
\(1,\)
\(\dfrac{5}{7}và\dfrac{6}{8}\)
\(\dfrac{5}{7}=\dfrac{5.8}{7.8}=\dfrac{40}{56};\dfrac{6}{8}=\dfrac{6.7}{8.7}=\dfrac{42}{56}\) vì \(\dfrac{40}{56}< \dfrac{42}{56}\) hay \(\dfrac{5}{7}< \dfrac{6}{8}\)
_______________
\(\dfrac{3}{8}và\dfrac{17}{49}\)
\(\dfrac{3}{8}=\dfrac{3.49}{8.49}=\dfrac{147}{392};\dfrac{17}{49}=\dfrac{17.8}{49.8}=\dfrac{136}{392}\) vì \(\dfrac{147}{392}>\dfrac{136}{392}\) hay \(\dfrac{3}{8}>\dfrac{17}{49}\)
_______________
\(\dfrac{47}{15}và\dfrac{65}{21}\)
\(\dfrac{47}{15}=\dfrac{47.7}{15.7}=\dfrac{329}{105};\dfrac{65}{21}=\dfrac{65.5}{21.5}=\dfrac{325}{105}\) vì \(\dfrac{329}{105}>\dfrac{325}{105}\)hay \(\dfrac{47}{15}>\dfrac{65}{21}\)
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\(\dfrac{23}{28}và\dfrac{24}{27}\)
\(\dfrac{23}{28}=\dfrac{23.27}{28.27}=\dfrac{621}{756};\dfrac{24}{27}=\dfrac{24.28}{27.28}=\dfrac{672}{756}\) vì \(\dfrac{621}{756}< \dfrac{672}{756}\) hay \(\dfrac{23}{28}< \dfrac{24}{27}\)
______________
\(\dfrac{29}{43}và\dfrac{5}{7}\)
\(\dfrac{29}{43}=\dfrac{29.7}{43.7}=\dfrac{203}{301};\dfrac{5}{7}=\dfrac{5.43}{7.43}=\dfrac{215}{301}\) vì \(\dfrac{203}{301}< \dfrac{215}{301}\) hay \(\dfrac{29}{43}< \dfrac{5}{7}\)
\(2,\)
\(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{32}\)
\(=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{16}\)
\(=\dfrac{4}{8}+\dfrac{2}{8}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{16}\)
\(=\dfrac{4+2+1}{8}+\dfrac{1}{16}+\dfrac{1}{16}\)
\(=\dfrac{7}{8}+\dfrac{1}{8}\)
\(=\dfrac{7+1}{8}=\dfrac{8}{8}=1\)
_______________________
\(\dfrac{1}{50.51}+\dfrac{1}{51.52}+\dfrac{1}{52.53}+...+\dfrac{1}{99.100}\)
\(=\dfrac{1}{50}-\dfrac{1}{51}+\dfrac{1}{51}-\dfrac{1}{52}+\dfrac{1}{52}-\dfrac{1}{53}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(=\dfrac{1}{50}-\dfrac{1}{100}\)
\(=\dfrac{2-1}{100}=\dfrac{1}{100}\)
4 và 5
