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Đặt \(A=\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+\dfrac{3}{11.14}\)
\(A=\dfrac{3}{2}-\dfrac{3}{5}+\dfrac{3}{5}-\dfrac{3}{8}+\dfrac{3}{8}-\dfrac{3}{11}+\dfrac{3}{11}-\dfrac{3}{14}\)
\(A=\dfrac{3}{2}-\dfrac{3}{14}\)
\(A=\dfrac{21}{14}-\dfrac{3}{14}\)
\(A=\dfrac{18}{14}\)
\(A=\dfrac{9}{7}\)
\(A=1\dfrac{2}{7}\)
\(B=\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+...+\dfrac{3}{26\cdot29}\)
\(B=\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{29}\)
\(B=\dfrac{1}{2}-\dfrac{1}{29}\)
\(B=\dfrac{27}{58}\)
B= 3/2x5 + 3/5x8+ 3/8x11 + ... + 3/26x29
B= 1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 + ... + 1/26 - 1/29
B= 1/2-1/29
B=27/58
\(\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{2006.2009}\)
\(=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{2006}-\frac{1}{2009}\)
\(=\frac{1}{5}-\frac{1}{2009}\)
\(=\frac{2004}{10045}\)
Đề: Tính
\(A=\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{2006.2009}\)
\(=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{2006}-\frac{1}{2009}\)
\(=\frac{1}{5}-\frac{1}{2009}=\frac{2004}{10045}\)
Vậy \(A=\frac{2004}{10045}.\)