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TA CÓ:
a; 1313/2121=13/21 165165/143143=165/143 424242/151515=42/15
=> 13/21 x 165/143 x 42/15=13 x 165 x 42/21 x 143 x 15=22/11=2
b,1995/1995 x 19961996/19931993 x 199319931993/199519951995
=1 x 1996/1993 x 1993/1995
=1 x 1996/1995
=1996/1995
a, 1313/2121 x 165165/143143 x 424242/151515
=13/21 x 165/143 x 13/5
=2
\(\frac{1995}{1996}.\frac{19961996}{19311931}.\frac{19311931}{19951995}=\frac{1995}{1996}.\frac{1996}{1931}.\frac{1931}{1995}=1\)
\(\frac{1313}{2121}.\frac{165165}{143143}.\frac{424242}{151515}=\frac{13}{21}.\frac{165}{143}.\frac{42}{15}=\frac{1}{1}.\frac{11}{11}.\frac{2}{1}=2\)
Tinh bang cach thuan tien:
1313 165165 424242
------- x ------------- x ------------
2121 143143 151515
\(\frac{1313}{2121}\)x\(\frac{165165}{143143}\)x\(\frac{424242}{151515}\)
=\(\frac{13x101}{21x101}\)X\(\frac{165x1001}{143x1001}\)X\(\frac{42x10101}{15x10101}\)
=\(\frac{13}{21}\)x\(\frac{165}{143}\)x\(\frac{42}{15}\)
=\(\frac{13}{21}\)x\(\frac{15}{13}\)x\(\frac{14}{5}\)
=\(\frac{13x15x14}{21x13x5}\)
=2
\(\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}\)
\(=\frac{5-2}{2\times5}+\frac{8-5}{5\times8}+\frac{11-8}{8\times11}+\frac{14-11}{11\times14}\)
\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}\)
\(=\frac{1}{2}-\frac{1}{14}=\frac{7}{14}-\frac{1}{14}=\frac{6}{14}=\frac{3}{7}\)
\(=\dfrac{12}{21}\cdot\dfrac{165}{143}\cdot\dfrac{1993}{1995}\)
\(=\dfrac{4}{7}\cdot\dfrac{15}{13}\cdot\dfrac{1993}{1995}=\dfrac{1993}{13}\cdot\dfrac{4}{931}=\dfrac{7972}{12103}\)