Question

Tính : B = 3/1+3/3+3/6+..............+3/210

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Answer 1

\(B=\frac{3}{1}+\frac{3}{3}+\frac{3}{6}+...+\frac{3}{210}\)

\(=\frac{6}{2}+\frac{6}{6}+\frac{6}{12}+...+\frac{6}{420}\)

\(=\frac{6}{1.2}+\frac{6}{2.3}+\frac{6}{3.4}+...+\frac{6}{20.21}\)

\(=6\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{20}-\frac{1}{21}\right)\)

\(=6\left(1-\frac{1}{21}\right)\)

\(=6.\frac{20}{21}=\frac{40}{7}\)