Question

\(\frac{4}{1.2}+\frac{4}{2.3}+...+\frac{4}{2014.2015}\)

Mình chỉ cần đáp án thôi ....( có lòi giải càng tốt )

Answer 1

\(\frac{4}{1\cdot2}+\frac{4}{2\cdot3}+...+\frac{4}{2014\cdot2015}\)

\(=4\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+....+\frac{1}{2014\cdot2015}\right)\)

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

\(=4\left(1-\frac{1}{2015}\right)\)

\(=4\cdot\frac{2014}{2015}=\frac{8056}{2015}\)