Tính nhanh 5/6+11/12+19/20+29/30+41/42+55/56+71/72

0 bình luận về “Tính nhanh 5/6+11/12+19/20+29/30+41/42+55/56+71/72”

1. $\frac{5}{6} + \frac{11}{12} + \frac{19}{20} + \frac{29}{30} + \frac{41}{42} + \frac{55}{56} + \frac{71}{72}\\= 1 – \frac{1}{6} + 1 – \frac{1}{12} + 1 – \frac{1}{20} + 1 – \frac{1}{30} + 1 – \frac{1}{42} + 1 – \frac{1}{56} + 1 – 1\frac{1}{72}\\= ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) – ( \frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \frac{1}{30} + \frac{1}{42} + \frac{1}{56} + \frac{1}{72} )\\=   7 – ( \frac{1}{12} . 3 + 1\frac{1}{3} .4 + \frac{1}{4} . 5 + \frac{1}{5} . 6 + \frac{1}{6} . 7 + \frac{1}{7} . 8 + \frac{1}{8} . 9 )\\=   7 – (\frac{1}{2} – \frac{1}{3} + \frac{1}{3} – \frac{1}{4} + \frac{1}{4} – \frac{1}{5} + \frac{1}{5} – \frac{1}{6} + \frac{1}{6} – \frac{1}{7} + \frac{1}{7} – \frac{1}{8} + \frac{1}{8} – \frac{1}{9})\\=   7 – \frac{7}{8}=\frac{119}{18}$

    

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2.   5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72

   = 1 – 1/6 + 1 – 1/12 + 1 – 1/20 + 1 – 1/30 + 1 – 1/42 + 1 – 1/56 + 1 – 1/72

   = ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) – ( 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 )

   =   7 – ( 1/2 x 3 + 1/3 x 4 + 1/4 x 5 + 1/5 x 6 + 1/6 x 7 + 1/7 x 8 + 1/8 x 9 )

   =   7 – (1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + 1/5 – 1/6 + 1/6 – 1/7 + 1/7 – 1/8 + 1/8 – 1/9)

   =   7 – ( 1/2 – 1/9 )

   =   7 – ( 9/18 – 2/18 )

   =   7 – 7/18

   =   126/18 – 7/18

   =    119/18

    

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