Cho S = \(-\frac{4}{1}.\frac{4}{5}-\frac{4}{5}.\frac{4}{9}-\frac{4}{9}.\frac{4}{13}-...-\frac{4}{2013}.\frac{4}{2017}\) Vậy, 2017S bằng bao nhiêu ?
Những câu hỏi liên quan
Cho S = \(-\frac{4}{1}.\frac{4}{5}-\frac{4}{5}.\frac{4}{9}-.......-\frac{4}{2013}.\frac{4}{2017}\)
Hỏi 2017S = ........
MN trình bày giùm mình nha Arigato ( cúi đầu)
Ta có : S= - 4/1 .4/5 - 4/5 .4/9-...- 4/2013 .4/2017
= -4 .( 4/1.5+4/5.9+...+4/2013.2017 )
= -4 . (1-1/5+1/5-1/9+...+1/2013-1/2017 )
= -4 . (1-1/2017)
= -4 .2016/2017
= -8064/2017
=> 2017S= -8064/2017 .2017 = -8064
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Tính \(S=-\frac{4}{1}.\frac{4}{5}-\frac{4}{5}.\frac{4}{9}-\frac{4}{9}-\frac{4}{13}-...-\frac{4}{2013}.\frac{4}{2017}\)
Cho S=\(-\frac{4}{1}\).\(\frac{4}{5}\)\(-\frac{4}{5}\).\(\frac{4}{9}\)\(-\frac{4}{9}\).\(\frac{4}{13}\)\(-\)....\(-\frac{4}{2013}\).\(\frac{4}{2017}\)
Vậy 2017S=...........
Cho S = -\(\frac{4}{1}\). \(\frac{4}{5}\)-\(\frac{4}{5}\). \(\frac{4}{9}\)-\(\frac{4}{9}\).\(\frac{4}{13}\)-....- \(\frac{4}{2013}\).\(\frac{4}{2017}\)
Tính 2017S
Tính S = \(\frac{-4}{1}\). \(\frac{4}{5}\)- \(\frac{4}{5}\). \(\frac{4}{9}\)- \(\frac{4}{9}\). \(\frac{4}{13}\) -...- \(\frac{4}{2013}\). \(\frac{4}{2017}\)
Rút gọn
1. \(\frac{5}{9}.\frac{7}{13}+\frac{5}{9}.\frac{9}{13}-\frac{5}{9}.\frac{3}{13}\)
2. \(\left(\frac{1+\frac{1}{5}+\frac{1}{7}+\frac{1}{11}}{2+\frac{2}{5}+\frac{2}{7}+\frac{2}{17}}:\frac{4-\frac{4}{7}+\frac{4}{9}-\frac{4}{13}}{1-\frac{1}{7}+\frac{1}{9}-\frac{1}{13}}\right):\frac{838383}{808080}\)
1. \(\frac{5}{9}.\frac{7}{13}+\frac{5}{9}.\frac{9}{13}-\frac{5}{9}.\frac{3}{13}\)
= \(\frac{5}{9}\) .(\(\frac{7}{13}+\frac{9}{13}-\frac{3}{13}\) )
= \(\frac{5}{9}\) . 1 = \(\frac{5}{9}\)
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\(\left(-1\frac{1}{6}\right)\left(\frac{1-\frac{3}{5}+\frac{3}{11}-\frac{3}{13}}{\frac{1}{3}-\frac{1}{5}+\frac{1}{11}-\frac{1}{13}}\right):\left(\frac{4-\frac{4}{17}+\frac{4}{19}-\frac{4}{2013}}{5-\frac{5}{17}+\frac{5}{19}-\frac{5}{2013}}\right)\)
tính
\(\left(-1\frac{1}{6}\right)\left(\frac{1-\frac{3}{5}+\frac{3}{11}-\frac{3}{13}}{\frac{1}{3}-\frac{1}{5}+\frac{1}{11}-\frac{1}{13}}\right)\left(\frac{4-\frac{4}{17}+\frac{4}{19}-\frac{4}{2013}}{5-\frac{5}{7}+\frac{5}{19}-\frac{5}{2013}}\right)\)
\(=-\frac{7}{6}.\left(\frac{3\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{11}-\frac{1}{13}\right)}{\frac{1}{3}-\frac{1}{5}+\frac{1}{11}-\frac{1}{13}}\right):\left(\frac{4.\left(1-\frac{1}{7}+\frac{1}{19}-\frac{1}{2013}\right)}{5.\left(1-\frac{1}{7}+\frac{1}{19}-\frac{1}{2013}\right)}\right)\)
\(=-\frac{7}{6}.3:\frac{4}{5}=-\frac{7}{2}.\frac{5}{4}=-\frac{35}{8}\)
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frac{1}{3}-frac{3}{5}+frac{5}{7}-frac{7}{9}+frac{9}{11}-frac{11}{13}+frac{11}{15}+frac{11}{13}-frac{9}{11}+frac{7}{9}-frac{5}{7}+frac{3}{5}-frac{1}{3}frac{-3}{4}.31frac{11}{23}-0,75.8frac{12}{28}left(2frac{1}{3}+3frac{1}{2}right):left(-4frac{1}{6}+3frac{1}{7}right)+7frac{1}{2}4frac{5}{9}:left(-frac{5}{7}right)+5frac{4}{9}:left(-frac{5}{7}right)frac{2}{3}-4left(frac{1}{2}+frac{3}{4}right)left(1-frac{1}{2}right).left(1-frac{1}{3}right).left(1-frac{1}{4}right)....left(1-frac{1}{n+1}right)nin Z
Đọc tiếp
\(\frac{1}{3}-\frac{3}{5}+\frac{5}{7}-\frac{7}{9}+\frac{9}{11}-\frac{11}{13}+\frac{11}{15}+\frac{11}{13}-\frac{9}{11}+\frac{7}{9}-\frac{5}{7}+\frac{3}{5}-\frac{1}{3}\)\(\frac{-3}{4}.31\frac{11}{23}-0,75.8\frac{12}{28}\)\(\left(2\frac{1}{3}+3\frac{1}{2}\right):\left(-4\frac{1}{6}+3\frac{1}{7}\right)+7\frac{1}{2}\)\(4\frac{5}{9}:\left(-\frac{5}{7}\right)+5\frac{4}{9}:\left(-\frac{5}{7}\right)\)\(\frac{2}{3}-4\left(\frac{1}{2}+\frac{3}{4}\right)\)\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)....\left(1-\frac{1}{n+1}\right)n\in Z\)
Tìm x:
\(\frac{\left(13\frac{2}{9}-15\frac{2}{3}\right)\cdot\left(30^2-5^4\right)}{\left(18\frac{3}{7}-17\frac{1}{4}\right)\cdot\left(25-12\cdot5^2\right)}\cdot x=\frac{\frac{2}{11}+\frac{3}{13}+\frac{4}{15}+\frac{5}{17}}{4\frac{1}{11}+\frac{5}{13}+\frac{9}{15}+\frac{13}{17}}\)