Question

Bài 3 .Tính:

a) A = 2/1x5 + 2/5x9 + 2/9x13 +....+2/81x85

b)B = 3/4x9 + 3/9x14 + 3/14x19 +....+ 3/34x39

c)C = 5/11x14 + 5/14x17 + 5/17x20 +....+ 5/47x50

Đây là một dang tính nhanh phân số bằng cách rút gọn.Mời các bạn thử ngẫm.

Answer 1

\(A=\frac{2}{1.5}+\frac{2}{5.9}+\frac{2}{9.13}+....+\frac{2}{81.85}\)

\(\Rightarrow2A=\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+....+\frac{4}{81.85}\)

\(\Rightarrow2A=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+....+\frac{1}{81}-\frac{1}{85}\)

\(\Rightarrow2A=1-\frac{1}{85}\)

\(\Rightarrow A=\frac{84}{85}:2=\frac{42}{85}\)

Answer 2

tính A còn lại tự tính nha

a) A = 2/1x5 + 2/5x9 + 2/9x13 +....+2/81x85

\(\frac{2}{1x5}+\frac{2}{5x9}+\frac{2}{9x13}+...+\frac{2}{81x85}\)

\(A=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{81}-\frac{1}{85}\)

\(A=1-\frac{1}{85}\)

\(\Rightarrow A=\frac{84}{85}\)

k nha

Answer 3

A = \(\frac{2}{1\cdot5}\) + \(\frac{2}{5\cdot9}\) + \(\frac{2}{9\cdot13}\) + ... + \(\frac{2}{81\cdot85}\)

   = \(\frac{1}{2}\) *  ( \(\frac{1}{1\cdot5}\) + \(\frac{1}{5\cdot9}\) + \(\frac{1}{9\cdot13}\) + ... + \(\frac{1}{81\cdot85}\) )

   = \(\frac{1}{2}\) * ( 1 - \(\frac{1}{5}\) + \(\frac{1}{5}\) - \(\frac{1}{9}\) + \(\frac{1}{9}\) - \(\frac{1}{13}\) + ... + \(\frac{1}{81}\) - \(\frac{1}{85}\) )

   = \(\frac{1}{2}\) * ( 1 - \(\frac{1}{85}\) )

   = \(\frac{1}{2}\) * \(\frac{84}{85}\)

   = \(\frac{42}{85}\)

Answer 4

\(B=\frac{3}{4.9}+\frac{3}{9.14}+\frac{3}{14.19}+.....+\frac{3}{47.50}\)

\(\Rightarrow B=\frac{3}{5}.\left(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+....+\frac{5}{47.50}\right)\)

\(\Rightarrow B=\frac{3}{5}.\left(\frac{1}{4}-\frac{1}{50}\right)\)

\(\Rightarrow B=\frac{3}{5}.\frac{23}{100}=\frac{69}{500}\)

Answer 5

B = \(\frac{3}{4\cdot9}+\frac{3}{9\cdot14}+\frac{3}{14\cdot19}+...+\frac{3}{34\cdot39}\)

   =  \(\frac{3}{5}\times\left(\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\frac{1}{14\cdot19}+...+\frac{1}{34\cdot39}\right)\)

   = \(\frac{3}{5}\times\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+...+\frac{1}{34}-\frac{1}{39}\right)\)

  = \(\frac{3}{5}\times\left(\frac{1}{4}-\frac{1}{39}\right)\)

  = \(\frac{3}{5}\times\frac{35}{156}\)

  = \(\frac{7}{52}\)

Answer 6

C = \(\frac{5}{11\cdot14}+\frac{5}{14\cdot17}+\frac{5}{17\cdot20}+...+\frac{5}{47\cdot50}\)

   = \(\frac{5}{3}\times\left(\frac{1}{11\cdot14}+\frac{1}{14\cdot17}+\frac{1}{17\cdot20}+...+\frac{1}{47\cdot50}\right)\)

   = \(\frac{5}{3}\times\left(\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}+...+\frac{1}{47}-\frac{1}{50}\right)\)

   = \(\frac{5}{3}\times\left(\frac{1}{11}-\frac{1}{50}\right)\)

   = \(\frac{5}{3}\times\frac{39}{550}\)

   = \(\frac{13}{110}\)

Answer 7

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