Question

Tính: A =\(\frac{4}{1\cdot2}+\frac{4}{2\cdot3}+\frac{4}{3\cdot4}+...+\frac{4}{2014\cdot2015}\)

Answer 1

Vậy \(A=\frac{8056}{2015}\)

Answer 2

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Answer 3

\(A=\frac{4}{1\cdot2}+\frac{4}{2\cdot3}+\frac{4}{3\cdot4}+...+\frac{4}{2014\cdot2015}\)

\(\frac{1}{4}A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2014\cdot2015}\)

\(\frac{1}{4}A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{2014}-\frac{1}{2015}\)

\(\frac{1}{4}A=1-\frac{1}{2015}\)

\(\frac{1}{4}A=\frac{2014}{2015}\)

\(A=\frac{2014}{2015}:\frac{1}{4}=\frac{2014}{2015}\cdot4=\frac{8056}{2015}\)