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\(15-\frac{15}{7}-\frac{15}{12}=11\frac{17}{28}\)
\(=\frac{325}{28}\)
\(3-\frac{3}{7}-\frac{3}{13}=2\frac{31}{91}\)
\(=\frac{213}{91}\)
1+7+8+15+23+.......+160
= 1+7+8+15+23+38+61+99+160
= 1+(8-1)+(15-7)+(23-8)+(38-15)+(61-23)+(99-38)+(160-61)+(259-99)
Gạch bỏ 8 với -8; 1 với -1; 5 với -5;..........60 với -60
= -7+160+259 = 412
\(\frac{15-\frac{15}{7}-\frac{15}{12}}{3-\frac{3}{7}-\frac{3}{12}}\)
= \(\frac{15.\left(1-\frac{1}{7}-\frac{1}{12}\right)}{3.\left(1-\frac{1}{7}-\frac{1}{12}\right)}\)
= \(\frac{15}{3}\)
= 5
\(a,=\frac{7-1}{1.3.7}+\frac{9-3}{3.7.9}+\frac{13-7}{7.9.13}+\frac{15-9}{9.13.15}\)\(+\frac{19-13}{13.15.19}\)
\(=\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.13}+\frac{1}{9.13}-\frac{1}{13.15}+\frac{1}{13.15}-\frac{1}{15.19}\)
\(=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}\)
\(b,=\frac{1}{6}.\left(\frac{6}{1.3.7}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\right)\)
làm giống như trên
\(c,=\frac{1}{8}.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{50-48}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{1}{2}-\frac{1}{2450}\right)=\frac{1}{16}.\left(\frac{1225}{2450}-\frac{1}{2450}\right)=\frac{153}{4900}\)
\(d,=\frac{5}{7}.\left(\frac{7}{1.5.8}+\frac{7}{5.8.12}+\frac{7}{8.12.15}+...+\frac{7}{33.36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{8-1}{1.5.8}+\frac{12-5}{5.8.12}+\frac{15-8}{8.12.15}+...+\frac{40-33}{33.36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{1}{1.5}-\frac{1}{5.8}+\frac{1}{5.8}-\frac{1}{8.12}+\frac{1}{8.12}-\frac{1}{12.15}+...+\frac{1}{33.36}-\frac{1}{36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{1}{5}-\frac{1}{1440}\right)=\frac{5}{7}.\left(\frac{288}{1440}-\frac{1}{1440}\right)=\frac{41}{288}\)
P/S: . là nhân nha
\(=\left(\frac{8}{15}-\frac{7}{15}\right)+\left(\frac{5}{12}-\frac{1}{12}\right)\)
\(=\frac{1}{15}+\frac{1}{3}\)
\(=\frac{6}{15}\)
\(=15,7\times1+15,7\times1+15,7\times1+15,7\times8-15,7\times1\\ =15,7\times\left(1+1+1+8-1\right)\\ 15,7\times10=157\)
`15,7+15,7+15,7+15,7xx8-15,7`
`=15,7xx3+15,7xx8-15,7xx1`
`=15,7xx(3+8-1)`
`=15,7xx10`
`=157`
`@An`