Thực hiện phép tính:
\(\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{780}\right)\)
Giúp mình nhé, xong trước ngày 13/2
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29 tháng 7 2017
\(B=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{780}\right)\)
\(\Rightarrow B=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{779}{780}\)
\(\Rightarrow B=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}.\frac{28}{30}...\frac{1558}{1560}\)
\(\Rightarrow B=\frac{1.4}{2.3}.\frac{2.5}{3.4}\frac{3.6}{4.5}...\frac{38.41}{39.40}\)
\(\Rightarrow B=\frac{\left(1.2.3...38\right)\left(4.5.6...41\right)}{\left(2.3.4...39\right)\left(3.4.5...40\right)}\)
\(\Rightarrow B=\frac{1.41}{39.3}=\frac{41}{117}\)
Vậy B=\(\frac{41}{117}\)
Ai thấy đúng thì k nha
27 tháng 6 2019
\(\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{6}\right)\cdot\cdot\cdot\left(1-\frac{1}{780}\right)\)
\(=\frac{2}{3}\cdot\frac{5}{6}\cdot\cdot\cdot\frac{779}{780}\)
\(=\frac{4}{6}\cdot\frac{10}{12}\cdot\cdot\cdot\frac{1578}{1560}\)
\(=\frac{1\cdot4}{2\cdot3}\cdot\frac{2\cdot5}{3\cdot4}\cdot\cdot\cdot\frac{38\cdot41}{39\cdot40}\)
\(=\frac{\left(1\cdot4\right)\cdot\left(2\cdot5\right)\cdot\cdot\cdot\left(38\cdot41\right)}{\left(2\cdot3\right)\cdot\left(3\cdot4\right)\cdot\cdot\cdot\left(39\cdot40\right)}\)
\(=\frac{\left(1\cdot2\cdot\cdot\cdot38\right)\cdot\left(4\cdot5\cdot\cdot\cdot41\right)}{\left(2\cdot3\cdot\cdot\cdot39\right)\cdot\left(3\cdot4\cdot\cdot\cdot40\right)}\)
\(=\frac{1\cdot41}{39\cdot3}\)
\(=\frac{41}{117}\)
Ta có: \(\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)....\left(1-\frac{1}{780}\right)\)
\(=\frac{2}{3}.\frac{5}{6}...\frac{779}{780}\)
\(=\frac{4}{6}.\frac{10}{12}....\frac{1558}{1560}\)
\(=\frac{1.4.2.5....38.41}{2.3.3.4....39.40}=\frac{\left(1.2.3..38\right)\left(4.5...41\right)}{\left(2.3.4...39\right)\left(3...40\right)}=\frac{41}{39.3}=\frac{41}{117}\)
\(\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)........\left(1-\frac{1}{780}\right)\)
\(=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}........\frac{779}{780}\)
\(=\frac{4}{6}.\frac{10}{12}\frac{18}{20}.\frac{28}{30}.........\frac{1558}{1560}\)
\(=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}.\frac{4.7}{5.6}...............\frac{38.41}{39.40}\)
\(=\frac{\left(1.2.3.4......38\right)\left(4.5.6.7..........41\right)}{\left(2.3.4.5.........39\right)\left(3.4.5.6.........40\right)}\)
\(=\frac{1.41}{39.3}\)
\(=\frac{41}{117}\)
Vậy \(\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)........\left(1-\frac{1}{780}\right)=\frac{41}{117}\)