Tính tổng:
\(M=-\frac{4}{1\cdot5}-\frac{4}{5\cdot9}-\frac{4}{9\cdot13}-...-\frac{4}{\left(n+4\right)\cdot n}\)
Những câu hỏi liên quan
\(\frac{4}{1\cdot3\cdot5}+\frac{4}{3\cdot5\cdot7}+\frac{4}{5\cdot7\cdot9}+\frac{4}{7\cdot9\cdot11}+\frac{4}{9\cdot11\cdot13}\)
giúp mk nha các bn
\(\frac{4}{1\cdot3\cdot5}+\frac{4}{3\cdot5\cdot7}+\frac{4}{5\cdot7\cdot9}+\frac{4}{7\cdot9\cdot11}+\frac{4}{9\cdot11\cdot13}\)
\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)
\(=\frac{1}{1.3}-\frac{1}{11.13}\)
\(=\frac{1}{3}-\frac{1}{143}\)
\(=\frac{140}{429}\)
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\(\frac{4\cdot x}{1\cdot5}\)+ \(\frac{4\cdot x}{5\cdot9}\) + \(\frac{4\cdot x}{9\cdot13}\) + \(\frac{4\cdot x}{13\cdot17}\) = 16
vậy x = ?
ai có cách giải bài này nhanh nhất thì giúp mình với ( dấu chấm ở giũa phép tính là giấu nhân )
gạch tất cả số 5, 9, 13
là bằng 4.x/1 + 4.x/17
rồi gợi ý thế thôi nhé
\(\frac{4.x}{1.5}+\frac{4.x}{5.9}+\frac{4.x}{9.13}+\frac{4.x}{13.17}=16\)
\(x.\left(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}\right)=16\)
\(x.\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}\right)=16\)
\(x.\left(1-\frac{1}{17}\right)=16\)
\(x.\frac{16}{17}=16\Rightarrow x=16:\frac{16}{17}=16.\frac{17}{16}\)
\(\Rightarrow x=17\)
Tính tổng : a) frac{1}{3cdot5cdot7}+frac{1}{5cdot7cdot9}+frac{1}{7cdot9cdot11}+...+frac{1}{2013cdot2015cdot2017} b) left(1-frac{1}{2^2}right)cdotleft(1-frac{1}{3^2}right)cdotleft(1-frac{1}{4^2}right)cdot...cdotleft(1-frac{1}{2017^2}right) c) left(1-frac{1}{1+2}right)cdotleft(1-frac{1}{1+2+3}right)cdot...cdotleft(1-frac{1}{1+2+3+...+2017}right)
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Tính tổng :
a) \(\frac{1}{3\cdot5\cdot7}+\frac{1}{5\cdot7\cdot9}+\frac{1}{7\cdot9\cdot11}+...+\frac{1}{2013\cdot2015\cdot2017}\)
b) \(\left(1-\frac{1}{2^2}\right)\cdot\left(1-\frac{1}{3^2}\right)\cdot\left(1-\frac{1}{4^2}\right)\cdot...\cdot\left(1-\frac{1}{2017^2}\right)\)
c) \(\left(1-\frac{1}{1+2}\right)\cdot\left(1-\frac{1}{1+2+3}\right)\cdot...\cdot\left(1-\frac{1}{1+2+3+...+2017}\right)\)
\(\left(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}\right)\cdot\left(x-\frac{1}{2}\right)=\frac{3}{4}\)
\(\frac{4}{1\cdot5}\)+\(\frac{4}{5\cdot9}\)+\(\frac{4}{9\cdot13}\)+\(\frac{4}{13\cdot17}\)+\(\frac{4}{17\cdot21}\)< 1
Áp dụng theo dạng toán số ai cập ta có:
4/1.5+4/5.9+4/9.13+4/13.17+4/17.21=1/1-1/5+1/5-1/9+1/9-1/13+1/13-1/17+1/17-1/21=1-1/21 < 1
Vậy tổng đó < 1
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Tính \(21\cdot\left(\frac{4}{1\cdot3}-\frac{8}{3\cdot5}+\frac{12}{5\cdot7}-\frac{16}{7\cdot9}+...+\frac{36}{17\cdot19}-\frac{40}{19\cdot21}\right)\)
\(\sqrt[2]{4\cdot9\frac{8}{8}+\frac{48\cdot11+5}{1\cdot\frac{814}{5+\frac{6145}{1\cdot\frac{821}{614}}}}}2548-\frac{8452}{14\cdot\frac{58}{96\cdot\frac{41}{\frac{24}{1\cdot\frac{975545}{1421+\frac{84874}{\frac{1+2+3+4+5+6+7+8+9\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9}{2\cdot\frac{2}{1}}}}}}}}\)
Tìm x:
\(\frac{\left(13\frac{2}{9}-15\frac{2}{3}\right)\cdot\left(30^2-5^4\right)}{\left(18\frac{3}{7}-17\frac{1}{4}\right)\cdot\left(25-12\cdot5^2\right)}\cdot x=\frac{\frac{2}{11}+\frac{3}{13}+\frac{4}{15}+\frac{5}{17}}{4\frac{1}{11}+\frac{5}{13}+\frac{9}{15}+\frac{13}{17}}\)
trình bày cách tính nhanh các phép tính sau đây
a)\(\frac{2^8\cdot6}{3^3\cdot5^4}:\frac{8^3\cdot9}{5^3\cdot3^3}-\left(2^{14}+3^{19}\right)\cdot\left(3^{81}+5^{64}\right)\left(2^4-4^2\right)\)
\(\frac{2^8\times6}{3^3\times5^4}\div\frac{8^3\times9}{5^3\times3^3}-\left(2^{14}+3^{19}\right)\left(3^{81}+5^{64}\right)\left(2^4-4^2\right)\)
\(=\frac{2^9\times3}{3^3\times5^4}\times\frac{5^3\times3^3}{2^9\times3^2}-\left(2^{14}+3^{19}\right)\left(3^{81}+5^{64}\right)\left(2^4-2^4\right)\)
\(=\frac{2^9\times3^4\times5^3}{3^5\times5^4\times2^9}-\left(2^{14}+3^{19}\right)\left(3^{81}+5^{64}\right)\times0\)
\(=\frac{1}{3\times5}-0\)
\(=\frac{1}{15}\)
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