\(\left(\frac{-1}{3.6}-\frac{1}{6.9}-\frac{1}{9.12}-\frac{1}{12.15}:\left|x\right|=\frac{-8}{15}\right)\)
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frac{4}{3.6}+ frac{4}{6.9}+ frac{4}{9.12}+frac{4}{12.15} 4(frac{1}{3.6}+frac{1}{6.9}+frac{1}{9.12}+frac{1}{12.15})frac{4}{3}( frac{1}{3}-frac{1}{6}+frac{1}{6}-frac{1}{9}+frac{1}{9}-frac{1}{12}+frac{1}{12}-frac{1}{15} )frac{4}{3}(frac{1}{3}-frac{1}{15})frac{4}{3}.frac{4}{15}frac{16}{45}mk làm đúng chưa
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\(\frac{4}{3.6}\)+ \(\frac{4}{6.9}\)+ \(\frac{4}{9.12}\)+\(\frac{4}{12.15}\)
= 4(\(\frac{1}{3.6}\)+\(\frac{1}{6.9}\)+\(\frac{1}{9.12}\)+\(\frac{1}{12.15}\))
=\(\frac{4}{3}\)( \(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+\frac{1}{12}-\frac{1}{15}\) )
=\(\frac{4}{3}\)(\(\frac{1}{3}-\frac{1}{15}\))
=\(\frac{4}{3}\).\(\frac{4}{15}\)
=\(\frac{16}{45}\)
mk làm đúng chưa
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Tính Nhanh : a) \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{99.101}\)
b) \(\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+\frac{1}{12.15}\)
a) Đặt \(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{99.101}\)
\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)
\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)
\(2A=1-\frac{1}{101}=\frac{100}{101}\)
\(A=\frac{100}{101}\div2=\frac{50}{101}\)
b) Đặt \(B=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+\frac{1}{12.15}\)
\(3B=\frac{3}{3.6}+\frac{3}{6.9}+\frac{3}{9.12}+\frac{3}{12.15}\)
\(3B=\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+\frac{1}{12}-\frac{1}{15}\)
\(3B=\frac{1}{3}-\frac{1}{15}=\frac{4}{15}\)
\(B=\frac{4}{15}\div3=\frac{4}{45}\)
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Đặt \(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{99.101}\)
\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)
\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)
\(2A=1-\frac{1}{101}=\frac{100}{101}\)
\(A=\frac{100}{101}\div2=\frac{50}{101}\)
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a) So sánh \(1995^n.1997^n\)với \(1996^{2n}\)
b) Rút gọn \(A=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+\frac{1}{12.15}+\frac{1}{15.18}+\frac{1}{18.21}+\frac{1}{21.24}\)
a/
\(1995^n.1997^n=\left(1995.1997\right)^n\)
\(1996^{2n}=\left(1996^2\right)^n\)
\(1995.1997=\left(1996-1\right).\left(1996+1\right)=1996^2-1\)
\(\Rightarrow1995.1997< 1996^2\Rightarrow1995^n.1997^n< 1996^{2n}\)
b/
\(A=\frac{1}{2.9}+\frac{1}{6.9}+\frac{1}{9.12}+\frac{1}{9.20}+\frac{1}{9.30}+\frac{1}{9.42}+\frac{1}{9.56}\)
\(A=\frac{1}{9}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\right)\)
\(A=\frac{1}{9}\left(\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{8-7}{7.8}\right)\)
\(A=\frac{1}{9}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}\right)\)
\(A=\frac{1}{9}\left(1-\frac{1}{9}\right)=\frac{1}{9}.\frac{8}{9}=\frac{8}{81}\)
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số số hạng của dãy\(\frac{1}{3.6};\frac{1}{6.9};\frac{1}{9.12};...;\frac{1}{156.159}\)là
Câu 1: Tính
a) A=\(\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).....\left(\frac{1}{98^2}-1\right).\left(\frac{1}{99^2}-1\right)\)
b) B=\(\frac{1}{2}:\left(-1\frac{1}{2}\right):1\frac{1}{3}:\left(-1\frac{1}{4}\right):1\frac{1}{5}:\left(-1\frac{1}{6}\right):...:\left(-1\frac{1}{100}\right)\)
c) C=\(\frac{4^6.9^5+6^9.120}{-8^4.3^{12}+6^4}\)
a)\(\left(1\frac{1}{3}\right)\left(1\frac{1}{8}\right)\left(1\frac{1}{15}\right)...\left(1\frac{1}{99}\right)\)
b)\(\left(1+\frac{1}{3}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{15}\right)\left(1+\frac{1}{24}\right)\left(1+\frac{1}{99}\right)\)
Tìm x biết \(1\frac{1}{30}:\left(24\frac{1}{6}-24\frac{1}{5}\right)-\left(1\frac{1}{2}-\frac{3}{4}\right):\left(4x-\frac{1}{2}\right)=\left(-1\frac{1}{15}\right):\left(8\frac{1}{5}-8\frac{1}{3}\right)\)
3,2.frac{15}{16}-left(75%+frac{2}{7}right):left(-1frac{1}{28}right)left(0,25+12,5-frac{5}{16}right):left[12-frac{7}{12}:left(frac{3}{8}-frac{1}{12}right)right]left(frac{-3}{5}+frac{5}{11}right):frac{-3}{7}+left(frac{-2}{5}+frac{6}{5}right):frac{-3}{7}14,5-frac{8}{9}:left(35-34frac{8}{9}right).frac{9}{8}1frac{1}{15}-left(frac{1}{15}+frac{4}{9}:frac{-2}{3}-frac{28}{16}.frac{6}{35}right)-frac{3}{10}Tìm x left(4,5-2xright)left(-3frac{2}{3}right)frac{11}{15}backslash34-xbackslashleft(-3right)^4left(4...
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\(3,2.\frac{15}{16}-\left(75\%+\frac{2}{7}\right):\left(-1\frac{1}{28}\right)\)
\(\left(0,25+12,5-\frac{5}{16}\right):\left[12-\frac{7}{12}:\left(\frac{3}{8}-\frac{1}{12}\right)\right]\)
\(\left(\frac{-3}{5}+\frac{5}{11}\right):\frac{-3}{7}+\left(\frac{-2}{5}+\frac{6}{5}\right):\frac{-3}{7}\)
\(14,5-\frac{8}{9}:\left(35-34\frac{8}{9}\right).\frac{9}{8}\)
\(1\frac{1}{15}-\left(\frac{1}{15}+\frac{4}{9}:\frac{-2}{3}-\frac{28}{16}.\frac{6}{35}\right)-\frac{3}{10}\)
Tìm x
\(\left(4,5-2x\right)\left(-3\frac{2}{3}\right)=\frac{11}{15}\)
\(\backslash34-x\backslash=\left(-3\right)^4\)
\(\left(4x^2-1\right)\left(\text{\x}\backslash-\frac{2}{3}\right)=0\)
\(\frac{3}{5}x-\frac{1}{2}\)\(x=\frac{-7}{20}\)
\(=\frac{16}{5}.\frac{15}{16}-\left(\frac{3}{4}+\frac{2}{7}\right):\left(\frac{-29}{28}\right)\)
\(=3-\left(\frac{21}{28}+\frac{8}{28}\right):\left(\frac{-29}{28}\right)\)
\(=3-\left(\frac{29}{28}\right).\left(\frac{-28}{29}\right)\)
\(=3-\left(-1\right)\)
\(=4\)
b) \(=\left(\frac{1}{4}+\frac{25}{2}-\frac{5}{16}\right):\left(12-\frac{7}{12}:\left(\frac{3}{8}-\frac{1}{12}\right)\right)\)
\(=\left(\frac{4}{16}+\frac{200}{16}-\frac{5}{16}\right):\left(12-\frac{7}{12}:\left(\frac{3.3}{2.3.4}-\frac{2}{2.3.4}\right)\right)\)
\(=\left(\frac{199}{16}\right):\left(12-\frac{7}{12}:\left(\frac{9}{24}-\frac{2}{24}\right)\right)\)
\(=\frac{199}{16}:\left(12-\frac{7}{12}.\frac{24}{7}\right)\)
\(=\frac{199}{16}:\left(12-2\right)\)
\(=\frac{199}{16}:10\)
\(=\frac{199}{160}\)
c) \(\left(\frac{-3}{5}+\frac{5}{11}\right):\frac{-3}{7}+\left(\frac{-2}{5}+\frac{6}{5}\right):\frac{-3}{7}\)
\(\left(\frac{-33}{55}+\frac{25}{55}\right):\frac{-3}{7}+\left(\frac{4}{5}\right):\frac{-3}{7}\)
\(\left(\frac{-8}{55}\right).\frac{-7}{3}+\frac{4}{5}.\frac{-7}{3}\)
\(\frac{-7}{3}\left(\frac{-8}{55}+\frac{4}{5}\right)\)
\(\frac{-7}{3}.\frac{36}{55}=\frac{-84}{55}\)
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nhớ làm giúp mình nhá mai mình phải đi học r :<
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tìm x,biết:a)frac{2}{left(x+2right)left(x+4right)}+frac{4}{left(x+4right)left(x+8right)}+frac{6}{left(x+8right)left(x+14right)}frac{x}{left(x+2right)left(x+14right)}b)frac{x+1}{10}+frac{x+1}{11}+frac{x+1}{12}frac{x+1}{13}+frac{x+1}{14}c)left(x+2right)^2frac{38}{25}+frac{9}{10}-frac{11}{15}+frac{13}{21}-frac{15}{28}+frac{17}{36}-...+frac{197}{4851}-frac{199}{4950}giúp tớ với,huhu
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tìm x,biết:
a)\(\frac{2}{\left(x+2\right)\left(x+4\right)}+\frac{4}{\left(x+4\right)\left(x+8\right)}+\frac{6}{\left(x+8\right)\left(x+14\right)}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)
b)\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)
c)\(\left(x+2\right)^2=\frac{38}{25}+\frac{9}{10}-\frac{11}{15}+\frac{13}{21}-\frac{15}{28}+\frac{17}{36}-...+\frac{197}{4851}-\frac{199}{4950}\)
giúp tớ với,huhu