Tính :
A = \(\frac{2}{3\times9}+\frac{5}{9\times24}+\frac{7}{24\times45}+\frac{2}{45\times51}+\frac{11}{51\times84}+\frac{13}{84\times123}\)
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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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\(\frac{3}{5\times9}+\frac{3}{9\times13}+\frac{3}{13\times17}+...+\frac{3}{37\times41}+\frac{3}{41\times45}\)
\(=\frac{3}{4}\left(\frac{1}{5.9}+\frac{1}{9.13}+...+\frac{1}{41.45}\right)\)
\(=\frac{3}{4}\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{41}-\frac{1}{45}\right)\)
\(=\frac{3}{4}\left(\frac{1}{5}-\frac{1}{45}\right)\)
\(=\frac{3}{4}\times\frac{8}{45}\)
\(=\frac{2}{15}\)
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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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Bài 1 : tìm x, biếta) left(frac{1}{4}-xright)left(x+frac{2}{5}right)0 bài 2 : Thực hiện các phép tính sau bằng cách hợp lí nếu có thể :a) left(frac{13}{24}-frac{29}{30}right):left(frac{-51}{5}right)bài 3 : tính nhanh A frac{1}{3}-frac{3}{4}-left(frac{-3}{5}right)+frac{1}{72}-frac{2}{9}-frac{1}{36}+frac{1}{15}B frac{1}{5}-frac{3}{7}+frac{5}{9}-frac{2}{11}+frac{7}{13}-frac{9}{16}-frac{7}{13}+frac{2}{11}-frac{5}{9}+frac{3}{7}-frac{1}{5}C frac{1}{100}-frac{1}{100.99}-frac{1}{99.98}-frac...
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Bài 1 : tìm x, biết
a) \(\left(\frac{1}{4}-x\right)\left(x+\frac{2}{5}\right)=0\)
bài 2 : Thực hiện các phép tính sau bằng cách hợp lí nếu có thể :
a) \(\left(\frac{13}{24}-\frac{29}{30}\right):\left(\frac{-51}{5}\right)\)
bài 3 : tính nhanh
A = \(\frac{1}{3}-\frac{3}{4}-\left(\frac{-3}{5}\right)+\frac{1}{72}-\frac{2}{9}-\frac{1}{36}+\frac{1}{15}\)
B = \(\frac{1}{5}-\frac{3}{7}+\frac{5}{9}-\frac{2}{11}+\frac{7}{13}-\frac{9}{16}-\frac{7}{13}+\frac{2}{11}-\frac{5}{9}+\frac{3}{7}-\frac{1}{5}\)
C = \(\frac{1}{100}-\frac{1}{100.99}-\frac{1}{99.98}-\frac{1}{98.97}-....-\frac{1}{3.2}-\frac{1}{2.1}\)
\(\left(\frac{1}{4}-x\right)\left(x+\frac{2}{5}\right)=0\)
Ta xét 2 trường hợp
\(\begin{cases}\frac{1}{4}-x=0\\x+\frac{2}{5}=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{1}{4}\\x=-\frac{2}{5}\end{cases}}\)
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tớ mới làm bài 1 thôi bài 2 3 tớ ko có thời gian
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Bài 1: Tìm x, biết:
\(\left(\frac{1}{4}-x\right)\left(x+\frac{2}{5}\right)=0\)
\(\Rightarrow\hept{\begin{cases}\frac{1}{4}-x=0\\x+\frac{2}{5}=0\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{1}{4}\\x=-\frac{2}{5}\end{cases}}}\)
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Tính nhanh:
a)\(\frac{24\cdot47-23}{24+47-23}\cdot\frac{3+\frac{3}{7}-\frac{3}{11}+\frac{3}{1001}-\frac{3}{13}}{\frac{9}{1001}-\frac{9}{13}+\frac{9}{7}-\frac{9}{11}+9}\)
b)\(\frac{1+2+2^2+...+2^{2012}}{2^{2014}-2}\)
\(\frac{24\cdot47-23}{24+47\cdot23}.\frac{3+\frac{3}{7}-\frac{3}{11}+\frac{3}{1001}-\frac{3}{13}}{\frac{9}{1001}-\frac{9}{13}+\frac{9}{7}-\frac{9}{11}+9}\)
\(=\frac{24\cdot\left(24+23\right)-23}{24+\left(24+23\right)\cdot23}\cdot\frac{3\left(1+\frac{1}{7}-\frac{1}{11}+\frac{1}{1001}-\frac{1}{13}\right)}{9\left(\frac{1}{1001}-\frac{1}{13}+\frac{1}{7}-\frac{1}{11}+1\right)}\)
\(=\frac{24^2+24\cdot23-23}{24+24\cdot23+23^2}\cdot\frac{3}{9}\) \(=\frac{24^2+23\cdot\left(24-1\right)}{\left(23+1\right)\cdot24\cdot23^2}\cdot\frac{1}{3}=1\cdot\frac{1}{3}=\frac{1}{3}\)
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Giúp mình với!!!!!
Tính:
G=\(\frac{1}{1\times3\times5}+\frac{1}{5\times7\times9}+\frac{1}{9\times11\times13}+...+\frac{1}{49\times51\times53}\)
\(\frac{1}{1x3x5}+\frac{1}{5x7x9}+\frac{1}{9x11x13}+.....+\frac{1}{49x51x53}=\)
\(1-\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}-\frac{1}{9}+.....+\frac{1}{49}-\frac{1}{51}-\frac{1}{53}=\)
\(1-\frac{1}{3}-\frac{1}{7}-....-\frac{1}{51}-\frac{1}{53}=\)
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Tính giá trị biểu thứca,Afrac{24cdot47-23}{24+47-23}cdotfrac{3+frac{3}{7}-frac{3}{11}+frac{3}{1001}-frac{3}{13}}{frac{9}{1001}-frac{9}{13}+frac{9}{7}-frac{9}{11}+9}b,Mfrac{1+2+2^2+2^3+...+2^{2012}}{2^{2014}-2}c,A81cdotleft[frac{12-frac{12}{7}-frac{12}{289}-frac{12}{85}}{4-frac{4}{7}-frac{4}{289}-frac{4}{85}}:frac{5+frac{5}{13}+frac{5}{169}+frac{5}{91}}{6+frac{6}{13}+frac{6}{169}+frac{6}{91}}right]:frac{158158158}{711711711}d,Afrac{5cdotleft(2^2.3^2right)^9cdotleft(2^2right)^6-2cdotleft(2^2cdot3r...
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Tính giá trị biểu thức
a,\(A=\frac{24\cdot47-23}{24+47-23}\cdot\frac{3+\frac{3}{7}-\frac{3}{11}+\frac{3}{1001}-\frac{3}{13}}{\frac{9}{1001}-\frac{9}{13}+\frac{9}{7}-\frac{9}{11}+9}\)
b,\(M=\frac{1+2+2^2+2^3+...+2^{2012}}{2^{2014}-2}\)
c,\(A=81\cdot\left[\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{5+\frac{5}{13}+\frac{5}{169}+\frac{5}{91}}{6+\frac{6}{13}+\frac{6}{169}+\frac{6}{91}}\right]:\frac{158158158}{711711711}\)
d,\(A=\frac{5\cdot\left(2^2.3^2\right)^9\cdot\left(2^2\right)^6-2\cdot\left(2^2\cdot3\right)^{14}\cdot3^4}{5\cdot2^{28}\cdot3^{18}-7\cdot2^{29}\cdot3^{18}}\)
bài 1 : tính phân số:a) frac{5}{7}+frac{4}{9}?;frac{4}{5}-frac{2}{3}?;frac{9}{11}+frac{3}{8}?;frac{16}{25}-frac{2}{5}??b)5+frac{3}{5}?;10-frac{9}{16}?;frac{2}{3}-left(frac{1}{6}+frac{1}{8}right)?c)frac{5}{7}+frac{7}{6}?;frac{7}{12}+frac{17}{18}?;frac{9}{8}+frac{15}{32}?;4+frac{35}{45}?d)frac{11}{4}-frac{15}{16}?;frac{5}{6}-frac{5}{8}?;frac{196}{64}-2?;3-frac{13}{9}?e)frac{8}{5}+frac{7}{6}+frac{5}{9}-2?;3-frac{5}{6}-frac{4}{9}+frac{32}{24}?
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bài 1 : tính phân số:
a) \(\frac{5}{7}+\frac{4}{9}=?;\frac{4}{5}-\frac{2}{3}=?;\frac{9}{11}+\frac{3}{8}=?;\frac{16}{25}-\frac{2}{5}=?\)=?
b)\(5+\frac{3}{5}=?;10-\frac{9}{16}=?;\frac{2}{3}-\left(\frac{1}{6}+\frac{1}{8}\right)=?\)
c)\(\frac{5}{7}+\frac{7}{6}=?;\frac{7}{12}+\frac{17}{18}=?;\frac{9}{8}+\frac{15}{32}=?;4+\frac{35}{45}=?\)
d)\(\frac{11}{4}-\frac{15}{16}=?;\frac{5}{6}-\frac{5}{8}=?;\frac{196}{64}-2=?;3-\frac{13}{9}=?\)
e)\(\frac{8}{5}+\frac{7}{6}+\frac{5}{9}-2=?;3-\frac{5}{6}-\frac{4}{9}+\frac{32}{24}=?\)
a)\(\dfrac{5}{7}+\dfrac{4}{9}=\dfrac{45}{63}+\dfrac{28}{63}=\dfrac{73}{63}\) ; \(\dfrac{9}{11}+\dfrac{3}{8}=\dfrac{72}{88}+\dfrac{33}{88}=\dfrac{105}{88}\)
\(\dfrac{4}{5}-\dfrac{2}{3}=\dfrac{12}{15}-\dfrac{10}{15}=\dfrac{2}{15}\); \(\dfrac{16}{25}-\dfrac{2}{5}=\dfrac{16}{25}-\dfrac{10}{25}=\dfrac{6}{25}\)
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Bài 3 , Thực hiện phép tính :
a, \(A=\frac{24\cdot47-23}{24+47-23}\cdot\frac{3+\frac{3}{7}+\frac{3}{11}+\frac{3}{1001}+\frac{3}{13}}{\frac{9}{1001}+\frac{9}{13}+\frac{9}{7}+\frac{9}{11}+9}\)
b, \(B=\frac{1+2+2^2+2^3+...+2^{2012}}{2^{2014}-2}\)
\(a)A=\frac{24\cdot47-23}{24+47-23}\cdot\frac{3+\frac{3}{7}+\frac{3}{11}+\frac{3}{1001}+\frac{3}{13}}{\frac{9}{1001}+\frac{9}{13}+\frac{9}{7}+\frac{9}{11}+9}\)
\(=\frac{(23+1)\cdot47-23}{24+47-23}\cdot\frac{3+\frac{3}{7}+\frac{3}{11}+\frac{3}{1001}+\frac{3}{13}}{\frac{9}{1001}+\frac{9}{13}+\frac{9}{7}+\frac{9}{11}+9}=\frac{47-23+24}{47-23+24}\cdot\frac{3(1+\frac{1}{7}+\frac{1}{11}+\frac{1}{1001}+\frac{1}{13})}{3(3+\frac{3}{1001}+\frac{3}{13}+\frac{3}{7}+\frac{3}{11})}\)
\(=\frac{1+\frac{1}{7}+\frac{1}{11}+\frac{1}{1001}+\frac{1}{13}}{3+\frac{3}{1001}+\frac{3}{13}+\frac{3}{7}+\frac{3}{11}}=\frac{1+\frac{1}{1001}+\frac{1}{13}+\frac{1}{7}+\frac{1}{11}}{3(1+\frac{1}{1001}+\frac{1}{13}+\frac{1}{7}+\frac{1}{11})}=\frac{1}{3}\)
\(b)\)\(\text{Đặt A = }1+2+2^2+2^3+...+2^{2012}\)
\(2A=2(1+2^2+2^3+...+2^{2012})\)
\(2A=2+2^2+2^3+...+2^{2013}\)
\(2A-A=(2+2^2+2^3+2^4+...+2^{2013})-(1+2+2^2+2^3+...+2^{2012})\)
\(\Rightarrow A=2^{2013}-1\)
\(\text{Quay lại bài toán,ta có :}\)
\(B=\frac{1+2+2^2+2^3+...+2^{2012}}{2^{2014}-2}=\frac{2^{2013}-1}{2^{2014}-2}=\frac{2^{2013}-1}{2(2^{2013}-1)}=\frac{1}{2}\)
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Tính nhanh:
\(B=\frac{1}{5}-\frac{3}{7}+\frac{5}{9}-\frac{2}{11}+\frac{7}{13}-\frac{9}{16}-\frac{7}{13}+\frac{2}{11}-\frac{5}{9}+\frac{3}{7}-\frac{1}{5}\)