tinh nhanh : 7/10 + 7/15 + 7/21 + .... + 7/120
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\(\frac{7}{13}.\left(\frac{7}{12}\right)-\frac{5}{12}.\left(\frac{21}{39}\right)+\frac{49}{91}.\left(\frac{8}{5}\right)=\frac{7}{13}.\left(\frac{7}{12}\right)-\frac{5}{12}.\left(\frac{7}{13}\right)+\frac{7}{13}.\left(\frac{8}{5}\right)=\frac{7}{13}.\left(\frac{7}{15}-\frac{5}{12}+\frac{8}{5}\right)=\frac{7}{13}.\left(\frac{33}{20}\right)=\frac{261}{260}\)
\(\frac{7}{8}=x-\frac{1}{10}-\frac{1}{15}-\frac{1}{21}-...-\frac{1}{120}\)
\(\frac{7}{4}=2x-\left(\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\right)\)
\(\frac{7}{4}=2x-2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right)\)
\(\frac{7}{4}=2x-2\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(\frac{7}{4}=2x-\frac{3}{8}\)
\(2x=\frac{17}{8}\)
\(x=\frac{17}{16}\)
Vậy \(x=\frac{17}{16}\)
\(=15,7\times1+15,7\times1+15,7\times1+15,7\times8-15,7\times1\\ =15,7\times\left(1+1+1+8-1\right)\\ 15,7\times10=157\)
\(\dfrac{7}{15}+\dfrac{4}{5}=\dfrac{7}{15}+\dfrac{12}{15}=\dfrac{19}{15}\)
\(\dfrac{2}{3}-\dfrac{3}{8}=\dfrac{16}{24}-\dfrac{9}{24}=\dfrac{7}{24}\)
\(\dfrac{4}{7}.\dfrac{21}{16}:\dfrac{5}{8}=\dfrac{4}{7}.\dfrac{21}{16}.\dfrac{8}{5}=\dfrac{4.3.7.4.2}{7.4.4.5}=\dfrac{6}{5}\)
\(A=\frac{4}{3.7}+\frac{4}{7.11}+...+\frac{4}{107.111}\)
\(A=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{107}-\frac{1}{111}\)
\(A=\frac{1}{3}-\frac{1}{111}\)
\(A=\frac{12}{37}\)
mà dài quá bạn ơi ban tách ra thành nhiều câu hỏi đi thế này trả lời lâu lắm