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\(S=\frac{3}{5.7}+\frac{3}{7.9}+.....+\frac{3}{59.61}\)
\(=\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+......+\frac{2}{59.61}\right)\)
=\(\frac{3}{2}.\left(\frac{7-5}{5.7}+\frac{9-7}{7.9}+......+\frac{61-59}{59.61}\right)\)
=\(\frac{3}{2}.\left(\frac{7}{5.7}-\frac{5}{5.7}+\frac{9}{7.9}-\frac{7}{7.9}+.....+\frac{61}{59.61}-\frac{59}{59.61}\right)\)
=\(\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.....+\frac{1}{59}-\frac{1}{61}\right)\)
=\(\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)\)
=\(\frac{3}{2}.\frac{56}{305}\)
=\(\frac{84}{305}\)
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\(\frac{3}{4}+\frac{5}{9}:\frac{4}{5}=\frac{3}{4}+\frac{5}{9}\times\frac{5}{4}\)
\(=\frac{3}{4}+\frac{25}{36}=\frac{27}{36}+\frac{25}{36}=\frac{27+25}{36}=\frac{52}{36}=\frac{13}{9}\)
\(\frac{7}{19}\times\frac{4}{7}-\frac{7}{19}\times\frac{3}{7}=\frac{7}{19}\times\left(\frac{4}{7}-\frac{3}{7}\right)\)
\(=\frac{7}{19}\times\frac{1}{7}=\frac{1}{19}\)
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A = 2/1.3 + 2/3.5 +.....+ 2/2003.2005
A = 1 - 1/3 + 1/3 - 1/5 +.....+ 1/2003 - 1/2005
A = 1 - 1/2005
A = 2004/2005
A= 1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+......+1/2001-1/2003+1/2003-1/2005
A= 1-1/2005 ( chỗ này ra như vậy bởi vì khi trừ cho 1/3 rồi cộng 1/3, trừ cho 1/5 rồi cộng 1/5......cũng k thay đổi giá trị cho nên các phần đó gạch bỏ và còn lại như kia thôi )
A= 2004/2005
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\(\frac{7}{9}\)x\(\frac{3}{14}\):\(\frac{5}{8}\)
= \(\frac{21}{126} : \frac{5}{8}\)
= \(\frac{7}{42}:\frac{5}{8}\)
= \(\frac{56}{210}\)= \(\frac{4}{15}\)
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4/7x9/5-3/7+4/7:5/6+6/7x2
=36/35-3/7+24/35+12/7
=36/35-15/35+24/35+60/35
=21/35+24/35+60/35
=45/35+60/35
=105/35
=3
\(\frac{3}{5}\times\frac{7}{9}+\frac{15}{18}\times\frac{2}{5}\)
\(=\frac{21}{45}+\frac{30}{90}\)
\(=\frac{4}{5}\)
#Hoktot#
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