\(\frac{3}{5\times9}+\frac{3}{9\times13}+\frac{3}{13\times17}+...+\frac{3}{37\times41}+\frac{3}{41\times45}\)
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Bài 9: Tìm x biết:
a, \(x+\frac{4}{5\times9}+\frac{4}{9\times13}+\frac{4}{13\times17}+....+\frac{4}{41\times45}=\frac{-37}{45}\)
b, \(x-\frac{20}{11\times13}-\frac{20}{13\times15}-\frac{20}{15\times17}-....-\frac{20}{53\times55}=\frac{3}{11}\)
c, \(\frac{1}{21}+\frac{1}{21}+\frac{1}{36}+.....+\frac{2}{x+\left(x+1\right)}=\frac{2}{9}\)
\(a,\)\(x+\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{41.45}=-\frac{37}{45}\)
\(x+\left(\frac{9-5}{5.9}+\frac{13-9}{9.13}+\frac{17-13}{13.17}+...+\frac{45-41}{41.45}\right)=-\frac{37}{45}\)
\(x+\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+....+\frac{1}{41}-\frac{1}{45}\right)-\frac{37}{45}\)
\(x+\left(\frac{1}{5}-\frac{1}{45}\right)=-\frac{37}{45}\)
\(x+\frac{8}{45}=-\frac{37}{45}\)
\(x=-\frac{37}{45}-\frac{8}{45}\)
\(x=-1\)
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\(S=\frac{1}{5\times9}+\frac{1}{9\times13}+\frac{1}{13\times17}+\frac{1}{17\times21}+\frac{1}{21\times25}\)
\(4S=\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{21}-\frac{1}{25}=\frac{1}{5}-\frac{1}{25}=\frac{4}{25}\)
\(S=\frac{4}{25}\times\frac{1}{4}=\frac{1}{25}\)
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\(4S=\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{21}-\frac{1}{25}=\frac{1}{5}-\frac{1}{25}=\frac{4}{25}\)
\(S=\frac{4}{25}\times\frac{1}{4}=\frac{1}{25}\)
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4S=1/5-1/9+1/9-1/13+1/13-1/17+1/17-1/21+1/21-1/25
4S=1/5-1/25
4S=4/25
S=4/25:4=1/25
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Xem thêm câu trả lời
bài 1 tínhQfrac{1}{2times9}+frac{1}{9times7}+frac{1}{7times19}+..............+frac{1}{252times509}Rfrac{1}{10times9}+frac{1}{18times13}+frac{1}{26times17}+...........+frac{1}{802times405}Sfrac{2}{4times7}-frac{3}{5times9}+frac{2}{7times10}-frac{3}{9times13}+..................+frac{2}{301times304}-frac{3}{401times403}ai nhanh nhất mik tick
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bài 1 tính
Q=\(\frac{1}{2\times9}\)+\(\frac{1}{9\times7}\)+\(\frac{1}{7\times19}\)+..............+\(\frac{1}{252\times509}\)
R=\(\frac{1}{10\times9}\)+\(\frac{1}{18\times13}\)+\(\frac{1}{26\times17}\)+...........+\(\frac{1}{802\times405}\)
S=\(\frac{2}{4\times7}\)\(-\)\(\frac{3}{5\times9}\)+\(\frac{2}{7\times10}\)\(-\)\(\frac{3}{9\times13}\)+..................+\(\frac{2}{301\times304}\)\(-\)\(\frac{3}{401\times403}\)
ai nhanh nhất mik tick
Tính :
A = \(\frac{2}{3\times9}+\frac{5}{9\times24}+\frac{7}{24\times45}+\frac{2}{45\times51}+\frac{11}{51\times84}+\frac{13}{84\times123}\)
\(3A=\frac{6}{3\times\left(3+6\right)}+\frac{15}{9\times\left(9+15\right)}+...+\frac{39}{84\times\left(84+39\right)}\)
\(=\frac{1}{3}-\frac{1}{9}+\frac{1}{9}-\frac{1}{24}+...+\frac{1}{84}-\frac{1}{123}=\frac{1}{3}-\frac{1}{123}=\frac{40}{123}\)
\(\Rightarrow A=\frac{40}{3.123}=\frac{40}{369}\)
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\(x-\left(\frac{20}{11\times13}+\frac{20}{13\times15}+\frac{20}{15\times17}+...+\frac{20}{53\times55}\right)=\frac{3}{11}\)
\(x-\left(\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\right)=\frac{3}{11}\)
\(x-10\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{53.55}\right)=\frac{3}{11}\)
\(x-10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
\(x-10\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)
\(x-10.\frac{4}{55}=\frac{3}{11}\)
\(x-\frac{40}{55}=\frac{3}{11}\)
\(x=\frac{3}{11}+\frac{40}{55}\)
\(x=\frac{55}{55}=1\)
nha.
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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 )
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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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Tính \(\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+\frac{1}{9\times11}+\frac{1}{11\times13}\)
SAI HẾT RỒI.........CẦN THÌ TỚ GIẢI LẠI CHO !!
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thế này :
= \(\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+......+\frac{2}{11.13}\right)\)
= \(\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{11}-\frac{1}{13}\right)\)
= \(\frac{1}{2}\left(\frac{1}{3}-\frac{1}{13}\right)\)
= \(\frac{1}{2}.\frac{10}{39}\)
= \(\frac{5}{39}\)
Vậy kq = \(\frac{5}{39}\)
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Tính: \(10101\times\left(\frac{5}{11111}+\frac{5}{22222}-\frac{4}{3\times7\times11\times13\times17}\right)\)
ko có cách nào tính ra đâu chỉ có thể bấm máy tính thôi
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\(\frac{3}{8\times11}+\frac{4}{11\times15}+\frac{5}{15\times20}+\frac{6}{20\times26}+\frac{7}{26\times33}+\frac{8}{33\times41}+\frac{9}{41\times50}=\frac{2}{5}-2\times x\)
làm ơn giúp em giải bài toán này!!!!!!!!
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