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Ta có:
\(\frac{1}{20.21}+\frac{1}{21.22}+\frac{1}{22.23}+...+\frac{1}{60.61}\)
\(=\frac{1}{20}-\frac{1}{21}+\frac{1}{21}-\frac{1}{22}+\frac{1}{22}-\frac{1}{23}+...+\frac{1}{60}-\frac{1}{61}\)
\(=\frac{1}{2}-\frac{1}{61}=\frac{59}{122}\)
b) \(\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{45.49}\)
\(=\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17}+...+\frac{1}{45.49}\)
\(=\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{45}-\frac{1}{49}\)
\(=\frac{1}{5}-\frac{1}{49}=\frac{44}{245}\)
Bn Tấn sai rùi
phần a , câu cuối là \(\frac{1}{20}\)chứ đâu phải \(\frac{1}{2}\)
\(\frac{2.4}{6.18}=\frac{1.2}{3.9}=\frac{2}{27}\)
\(\frac{3.5.7}{6.9.14}=\frac{1.5.7}{2.9.2}=\frac{35}{36}\)
\(\frac{4.7-4.5}{64}=\frac{4\left(7-5\right)}{64}=\frac{8}{64}=\frac{1}{8}\)
a)Từ 2b-a=3535
=>a=2b-3535
khi đó a+b=5252
<=>(2b-3535)+b=5252
<=>2b+b=5252+3535<=>3b=8787<=>b=2929
Mà a+b=5252=>a=5252-b=5252-2929=2323
Vậy p/s a/b=2323/2929
\(A=\frac{15.39}{9.25}=\frac{3.5.3.13}{3.3.5.5}=\frac{13}{5}\)
\(B=\frac{21-21.5}{2^2}=\frac{21.\left(1-5\right)}{4}=\frac{21.\left(-4\right)}{4}=-21\)
\(C=\frac{1.2.3....20}{2.4...40}=\frac{1.2.3...20}{2\left(1.2.3...20\right)}=\frac{1}{2}\)
Ta có :
\(A=\frac{15.39}{9.25}=\frac{3.5.39}{3^2.5^2}=\frac{39}{3.5}=\frac{39}{15}\)
\(B=\frac{21-21.5}{2^2}=\frac{21.\left(1-5\right)}{4}=\frac{21.\left(-4\right)}{4}=\frac{21.\left(-1\right)}{1}=-21\)
\(C=\frac{1.2.3...20}{2.4.6...40}=\frac{\left(1.3.5...19\right).\left(2.4.6...20\right)}{\left(2.4.6...20\right).\left(22.24.26...40\right)}=\frac{1.3.5.19}{22.24.26...40}\)
a) \(\frac{\left(-63\right)}{81}=\frac{\left(-63\right):9}{81:9}=\frac{-7}{9}\)
b) \(\frac{-25}{-75}=\frac{\left(-25\right):25}{\left(-75\right):25}=\frac{-1}{-3}=\frac{1}{3}\)
\(a.\frac{-63}{81}=\frac{-7}{9}\)
\(b.\frac{-25}{-75}=\frac{1}{3}\)
a)\(\frac{1}{4}\)(\(\frac{21.22+76.79+81.85}{21.22+76.79+81.85}\))=\(\frac{1}{4}\)
b)\(\frac{20052005}{20062006}\)=\(\frac{20052005:10001}{20062006:10001}\)=\(\frac{2005}{2006}\)