Question

chứng minh B = 36 / 1 x 3 x 5 + 36 / 3 x 5 x7 + 36 / 5 x 7 x 9 +  .... + 36 / 25 x 27 x29 < 3

 

Answer 1

\(B=\frac{36}{1.3.5}+\frac{36}{3.5.7}+\frac{36}{5.7.9}+...+\frac{36}{25.27.29}\)

   \(=9.\left(\frac{4}{1.3.5}+\frac{4}{3.5.7}+\frac{4}{5.7.9}+...+\frac{4}{25.27.29}\right)\)

    \(=9.\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+\frac{1}{5.7}-\frac{1}{7.9}+...+\frac{1}{25.27}-\frac{1}{27.29}\right)\)

    \(=9.\left(\frac{1}{3}-\frac{1}{675}\right)\)

    \(=9.\frac{224}{675}\)

    \(=\frac{224}{75}\)

Answer 2

THIẾU

\(=\frac{224}{75}< \frac{225}{75}=3\)

Vậy \(B< 3\)

Answer 3

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