Question

2/6+2/12+2/20+.............+2/210

Answer 1

Ta có:\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+..+\frac{2}{210}=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+..+\frac{2}{14.15}\)

\(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+..+\frac{1}{14}-\frac{1}{15}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{15}\right)\)

\(=1-\frac{2}{15}=\frac{15-2}{15}=\frac{13}{15}\)

Answer 2

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