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\(A=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)
\(\Leftrightarrow A=\frac{1}{1.3}-\frac{1}{11.13}=\frac{1}{3}-\frac{1}{143}=\frac{140}{429}\)
\(A=\frac{4}{1.3.5}+\frac{4}{3.5.7}+\frac{4}{5.7.9}+\frac{4}{7.9.11}+\frac{4}{9.11.13}\)
\(\Rightarrow A=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)
\(\Rightarrow A=\frac{1}{1.3}-\frac{1}{11.13}=\frac{1}{3}-\frac{1}{143}=\frac{140}{429}\)
Sửa đề:
\(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{28}{1995}\)
\(=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{285}\)
\(=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+\frac{4}{15.19}\)
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}\)
\(=\frac{1}{3}-\frac{1}{19}\)
\(=\frac{16}{57}\)
\(=\dfrac{60-14-11}{12}:\dfrac{9+4}{12}=\dfrac{35}{13}\)
(dấu . là dấu nhân )
a, \(\frac{3}{2}\cdot\frac{4}{7}+\frac{3}{7}\cdot\frac{3}{2}\)
= \(\frac{3}{2}\left(\frac{4}{7}+\frac{3}{7}\right)\)
=\(\frac{3}{2}\cdot\frac{7}{7}=\frac{3}{2}\)
b, \(\frac{12}{5}\cdot4-4\cdot\frac{7}{5}\)
=\(4\left(\frac{12}{5}-\frac{7}{5}\right)=4\cdot\frac{5}{5}=4\)
c, \(\frac{5}{11}:\frac{1}{2}+\frac{6}{11}:\frac{1}{2}\)
=\(2\left(\frac{5}{11}+\frac{6}{11}\right)=2\cdot\frac{11}{11}=2\)
a;3/2x(4/7+3/7)
=3/2x1
=3/2
b;12/5x4-4x7/5
=4x(12/5-7/5)
=4x1
=4
c;5/11:1/2+6/11:1/2
=1/2:(5/11+6/11)
=1/2:1
=1/2
b)\(\left(\dfrac{13}{21}\times\dfrac{7}{8}-\dfrac{12}{21}\times\dfrac{7}{8}\right)\times12\)
=\(\left(\dfrac{7}{8}\times\left(\dfrac{13}{21}-\dfrac{12}{21}\right)\right)\times12\)
=\(\left(\dfrac{7}{8}\times\dfrac{1}{21}\right)\times12\)
=\(\dfrac{7}{16}\)
c)\(\dfrac{7}{11}+\dfrac{3}{4}+\dfrac{4}{11}+\dfrac{8}{17}+\dfrac{1}{4}+\dfrac{18}{34}\)
= \(\left(\dfrac{7}{11}+\dfrac{4}{11}\right)+\left(\dfrac{3}{4}+\dfrac{1}{4}\right)+\dfrac{8}{17}+\dfrac{9}{17}\)
= 1 + 1 + \(\left(\dfrac{8}{17}+\dfrac{9}{17}\right)\)
= 2 + 1
= 3
a) 1/11 + 2/11 + 3/11 + ... + 10/11
= 1 + 2 + 3 + ... + 10 / 11
= (1 + 10).10:2 / 11
= 11.5/11
= 5
b) 1/10×20 + 1/20×30 + 1/30×40 + ... + 1/90×100
= 1/10×10 × (1/1×2 + 1/2×3 + 1/3×4 + ... + 1/9×10)
= 1/100 × (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/9 - 1/10)
= 1/100 × (1 - 1/10)
= 1/100 × 9/10
= 9/1000
\(\dfrac{11}{9}\) - \(\dfrac{4}{3}\) + \(\dfrac{7}{9}\)
= (\(\dfrac{11}{9}\) + \(\dfrac{7}{9}\)) - \(\dfrac{4}{3}\)
= \(\dfrac{18}{9}\) - \(\dfrac{4}{3}\)
= 2 - \(\dfrac{4}{3}\)
= \(\dfrac{2\times3}{3}\) - \(\dfrac{4}{3}\)
= \(\dfrac{6}{3}\) - \(\dfrac{4}{3}\)
= \(\dfrac{2}{3}\)
\((\)\(\dfrac{11}{9}\)+\(\dfrac{7}{9}\)\()\)-\(\dfrac{4}{3}\)
= 2-\(\dfrac{4}{3}\)
= \(\dfrac{2}{3}\)
\(\frac{6}{7}.\frac{11}{5}+\frac{11}{5}.\frac{4}{7}-\frac{2}{3}\)
=\(\left(\frac{6}{7}+\frac{4}{7}\right).\frac{11}{5}-\frac{2}{3}\)
=\(\frac{10}{7}.\frac{11}{5}-\frac{2}{3}\)
=\(\frac{52}{21}\)
