\(S=\frac{1}{5\times9}+\frac{1}{9\times13}+\frac{1}{13\times17}+\frac{1}{17\times21}+\frac{1}{21\times25}\)
Những câu hỏi liên quan
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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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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\(\frac{3}{5\times9}+\frac{3}{9\times13}+\frac{3}{13\times17}+...+\frac{3}{37\times41}+\frac{3}{41\times45}\)
\(=\frac{3}{4}\left(\frac{1}{5.9}+\frac{1}{9.13}+...+\frac{1}{41.45}\right)\)
\(=\frac{3}{4}\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{41}-\frac{1}{45}\right)\)
\(=\frac{3}{4}\left(\frac{1}{5}-\frac{1}{45}\right)\)
\(=\frac{3}{4}\times\frac{8}{45}\)
\(=\frac{2}{15}\)
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\(A=\frac{3}{5\cdot9}+\frac{3}{9\cdot13}+\frac{3}{13\cdot17}+...+\frac{3}{37\cdot41}+\frac{3}{41\cdot45}\)
\(\frac{4A}{3}=\frac{9-5}{5\cdot9}+\frac{13-9}{9\cdot13}+\frac{17-13}{13\cdot17}+...+\frac{41-37}{37\cdot41}+\frac{45-41}{41\cdot45}\)
\(\frac{4A}{3}=\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{37}-\frac{1}{41}+\frac{1}{45}-\frac{1}{45}\)
\(\frac{4A}{3}=\frac{1}{5}-\frac{1}{45}=\frac{9-1}{45}=\frac{8}{45}\Rightarrow A=\frac{8}{45}\cdot\frac{3}{4}=\frac{2}{15}\)
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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
6. Tìm s
a) s - \(\frac{20}{11\times13}-\frac{20}{13\times15}-\frac{20}{15\times17}-.....-\frac{20}{53\times55}=\frac{3}{11}\)
b) \(\frac{1}{21}+\frac{1}{28}+\frac{1}{39}+...+\frac{2}{s\left(s+1\right)}=\frac{2}{9}\)
( Toàn lớp 6 nha )
a) gt \(\Leftrightarrow\) s-\(10\times\left(\frac{2}{11\times13}+\frac{2}{13\times15}+...+\frac{2}{53\times55}\right)=\frac{3}{11}\)
\(\Leftrightarrow s-10\times\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
\(\Leftrightarrow S-10\times\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)
\(\Leftrightarrow S=1\)
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câu b hình như sai đề
Phải là \(\frac{1}{36}\) chứ ko phải \(\frac{1}{39}\)
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Xem thêm câu trả lời
\(\frac{1}{1\times5}+\frac{1}{5\times9}+\frac{1}{9\times13}+...+\frac{1}{97\times101}\)
\(\frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+.....+\frac{1}{97.101}\)
\(=\frac{1}{4}\left(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+......+\frac{4}{97.101}\right)\)
\(=\frac{1}{4}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+.....+\frac{1}{97}-\frac{1}{101}\right)\)
\(=\frac{1}{4}\left(1-\frac{1}{101}\right)\)
\(=\frac{1}{4}.\frac{100}{101}=\frac{25}{101}\)
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Tính hợp lí:
A=\(\frac{5}{12\times17}+\frac{35}{17\times18}-\frac{39}{18\times21}+\frac{30}{21\times72}\)
B=\(\frac{767676\times31-626262\times38}{1^2+2^3+3^4+......+99^{100}}\)
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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Tìm số nguyên âm x, biết:
\(^{x^2}-\left(\frac{3}{5}\right)^2=\frac{1}{1\times2}+\frac{1}{2\times7}+\frac{1}{5\times7}+\frac{1}{5\times13}+\frac{1}{8\times13}+\frac{1}{8\times19}+\frac{1}{11\times19}+\frac{1}{11\times19}+\frac{1}{11\times25}\)
AI NHANH MK TICK CHO NHA!