Tính \(S=-\frac{4}{1}.\frac{4}{5}-\frac{4}{5}.\frac{4}{9}-\frac{4}{9}-\frac{4}{13}-...-\frac{4}{2013}.\frac{4}{2017}\)
Những câu hỏi liên quan
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 ?
S=-4/1.4/5-4/5.4/9-4/9.4/13-...-4/2013.4/2017
=-4^2/1.5-4^2/5.9-4^2/9.13-...-4^2/2013.2017
=-4(4/1.5+4/5.9-4/9.13-...-4/2013.2017)
=-4(1-1/5+1/5-1/9+1/9-1/13-...-1/2013-1/2017)
=-4(1-1/2017)
=-4.2016/2017=-8064/2017
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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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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 = \(\frac{-4}{1}\). \(\frac{4}{5}\)- \(\frac{4}{5}\). \(\frac{4}{9}\)- \(\frac{4}{9}\). \(\frac{4}{13}\) -...- \(\frac{4}{2013}\). \(\frac{4}{2017}\)
\(\left(-1\frac{1}{6}\right)\left(\frac{1-\frac{3}{5}+\frac{3}{11}-\frac{3}{13}}{\frac{1}{3}-\frac{1}{5}+\frac{1}{11}-\frac{1}{13}}\right):\left(\frac{4-\frac{4}{17}+\frac{4}{19}-\frac{4}{2013}}{5-\frac{5}{17}+\frac{5}{19}-\frac{5}{2013}}\right)\)
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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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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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=...........
1. Tính:
a. \(75\%-1\frac{1}{2}.\frac{4}{3}+1,5:\frac{-9}{4}-\left(-\frac{1}{2}\right)^2\)
b. \(\frac{-4}{9}.\frac{6}{13}+7\frac{4}{9}-\frac{4}{9}:\frac{13}{7}-5\frac{4}{9}-2\)
2. Tìm x, biết:
a. \(x\in Z,-1\le\frac{x}{5}< 0\)
*làm nhanh nha, mk cần gấp lắm
1/ Tìm x :frac{xtimes2+5}{x+5}frac{6}{4}2/ Tính nhanh :a) frac{4}{1times5}+frac{4}{5times9}+frac{4}{9times13}+frac{4}{13times17}+frac{4}{17times21}b) left(1-frac{1}{2}right)timesleft(1-frac{1}{3}right)timesleft(1-frac{1}{4}right)times.......timesleft(1-frac{1}{2017}right)c) A2000-5-5-5-.......-5( có 200 số 5 )
Đọc tiếp
1/ Tìm x :
\(\frac{x\times2+5}{x+5}=\frac{6}{4}\)
2/ Tính nhanh :
a) \(\frac{4}{1\times5}+\frac{4}{5\times9}+\frac{4}{9\times13}+\frac{4}{13\times17}+\frac{4}{17\times21}\)
b) \(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times.......\times\left(1-\frac{1}{2017}\right)\)
c) \(A=2000-5-5-5-.......-5\)( có 200 số 5 )
2/
a) \(\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+\frac{4}{9\cdot13}+\frac{4}{13\cdot17}+\frac{4}{17\cdot21}\)
\(=\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+....+\frac{1}{17}-\frac{1}{21}\right)\)
\(=1-\frac{1}{21}=\frac{20}{21}\)
b) \(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{2017}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot..\cdot\frac{2016}{2017}\)
\(=\frac{1}{2017}\)
c) \(A=2000-5-5-5-..-5\)(có 200 số 5)
\(A=2000-\left(5\cdot200\right)\)
\(A=2000-1000\)
\(A=1000\)
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