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\(\dfrac{3}{4}+\dfrac{75}{100}\times299+75\%\times300+0,75\times400\)
\(=0,75+0,75\times299+0,75\times300+0,75\times400\)
\(=0,75\times\left(1+2999+300+400\right)=0,75\times1000=750\)
Tổng vận tốc của hai xe là 54+36=90(km/h)
Hai xe gặp nhau sau khi đi được:
225:90=2,5(giờ)=2h30p
Hai xe gặp nhau lúc:
6h30p+2h30p=9h
SAU SỐ GIỜ GẶP NHAU LÀ : 225 : ( 54 + 36 ) =2,5 h=2h30 p
Gặp nhau là : 6h30p+2h30p=9h
\(x:\dfrac{6}{5}=\dfrac{3}{5}\)
=>\(x=\dfrac{6}{5}\times\dfrac{3}{5}=\dfrac{18}{25}\)
\(S=\dfrac{3}{12}+\dfrac{3}{20}+\dfrac{3}{30}+\dfrac{3}{42}+\dfrac{3}{56}\)
\(=3\left(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\right)\)
\(=3\left(\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}\right)\)
\(=3\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\right)\)
\(=3\left(\dfrac{1}{3}-\dfrac{1}{8}\right)=1-\dfrac{3}{8}=\dfrac{5}{8}\)
\(P=\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{2023\cdot2025}\)
\(=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{2023\cdot2025}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2023}-\dfrac{1}{2025}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{2025}\right)=\dfrac{1}{2}\cdot\dfrac{2024}{2025}=\dfrac{1012}{2025}\)
\(A=1+\dfrac{1}{2}+...+\dfrac{1}{2^{2012}}\)
=>\(2A=2+1+...+\dfrac{1}{2^{2011}}\)
=>\(2A-A=2+1+...+\dfrac{1}{2^{2011}}-1-\dfrac{1}{2}-...-\dfrac{1}{2^{2012}}\)
=>\(A=2-\dfrac{1}{2^{2012}}=\dfrac{2^{2013}-1}{2^{2012}}\)
