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\(A=\dfrac{1}{5\times7}+\dfrac{1}{7\times9}+\dfrac{1}{9\times11}+...+\dfrac{1}{87\times89}\)
\(A=\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+...+\dfrac{1}{87}-\dfrac{1}{89}\)
\(A=\dfrac{1}{5}-\left(\dfrac{1}{7}-\dfrac{1}{7}\right)-\left(\dfrac{1}{9}-\dfrac{1}{9}\right)-...-\left(\dfrac{1}{87}-\dfrac{1}{87}\right)-\dfrac{1}{89}\)
\(A=\dfrac{1}{5}-\dfrac{1}{89}\)
\(A=\dfrac{84}{445}\)
Vậy, `A=84/445.`
A = \(\dfrac{1}{5\times7}\) + \(\dfrac{1}{7\times9}\)+\(\dfrac{1}{9\times11}\)+...+\(\dfrac{1}{87\times89}\)
A = \(\dfrac{1}{2}\) \(\times\)( \(\dfrac{2}{5\times7}\)+\(\dfrac{2}{7\times9}\)+\(\dfrac{2}{9\times11}\)+...+\(\dfrac{2}{87\times89}\))
A = \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{9}\) + \(\dfrac{1}{11}\) +...+ \(\dfrac{1}{87}\) - \(\dfrac{1}{89}\))
A = \(\dfrac{1}{2}\) \(\times\) (\(\dfrac{1}{5}\) - \(\dfrac{1}{89}\))
A = \(\dfrac{1}{2}\) \(\times\) \(\dfrac{84}{445}\)
A = \(\dfrac{42}{445}\)
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\(\dfrac{8}{9}\) < 1 = \(\dfrac{9}{9}\) (so sánh với 1)
\(\dfrac{8}{9}\) < \(\dfrac{9}{9}\)
\(\dfrac{6}{6}\) > \(\dfrac{6}{8}\) (hai phân số có cùng tử số phân số nào có mẫu nhỏ hơn thì phân số đó lớn hơn)
\(\dfrac{7}{8}\) = 1 - \(\dfrac{1}{8}\)
\(\dfrac{6}{7}\) = 1 - \(\dfrac{1}{7}\)
vì \(\dfrac{1}{8}\) < \(\dfrac{1}{7}\)
\(\dfrac{7}{8}\) > \(\dfrac{6}{7}\) (so sánh bằng phần bù, phân số nào có phần bù nhỏ hơn thì phân số đó lớn hơn)
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Lời giải:
$=\frac{16}{21}+\frac{2}{9}-\frac{2}{21}+\frac{3}{9}$
$=(\frac{16}{21}-\frac{2}{21})+(\frac{2}{9}+\frac{3}{9})$
$=\frac{14}{21}+\frac{5}{9}=\frac{2}{3}+\frac{5}{9}=\frac{11}{9}$
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\(1-1-3+2-4+7+6+8+9+9+0+7+7+0-9-7-9\)
\(=\left(1-1\right)+\left(7+7+7-7\right)+\left(9+9-9-9\right)+\left(2+8\right)+\left(-3-4+6\right)\)
\(=14+10-1\)
\(=23\)
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\(\dfrac{8}{9}:\dfrac{3}{7}=\dfrac{56}{27}\\ \dfrac{8}{9}+\dfrac{2}{5}=\dfrac{58}{45}\\ \dfrac{7}{8}-\dfrac{1}{3}=\dfrac{13}{24}\\ \dfrac{3}{10}\times\dfrac{1}{6}=\dfrac{1}{20}\\ 1\dfrac{2}{7}+6\dfrac{5}{6}=\dfrac{9}{7}+\dfrac{41}{6}=\dfrac{341}{42}\\ 5\dfrac{3}{4}-\dfrac{1}{5}=\dfrac{23}{4}-\dfrac{1}{5}=\dfrac{111}{20}\\ 6\dfrac{2}{9}:4\dfrac{7}{10}=\dfrac{56}{9}:\dfrac{47}{10}=\dfrac{560}{423}\\ \dfrac{5}{3}+\dfrac{3}{2}-\dfrac{7}{6}=2\)
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7/7 + 6/9 + 87/9 = 11.3333333333 nha
=714/63 nha bạn!