Question

[Chu Ngọc Ánh]

3 / 2 * 6 + 3/6*10 + 3/ 10 *14+....+ 3/ 26*30

Answer 1

[Xyz OLM]

\(\frac{3}{2.6}+\frac{3}{6.10}+\frac{3}{10.14}+...+\frac{3}{26.30}=\frac{3}{4}\left(\frac{4}{2.6}+\frac{4}{6.10}+\frac{4}{10.14}+...+\frac{4}{26.30}\right)\)

\(=\frac{3}{4}\left(\frac{1}{2}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+\frac{1}{10}-\frac{1}{14}+...+\frac{1}{26}-\frac{1}{30}\right)=\frac{3}{4}\left(\frac{1}{2}-\frac{1}{30}\right)\)

\(=\frac{3}{4}.\frac{7}{15}=\frac{7}{20}\)

Answer 2

[Quỳnh Anh]

Trả lời:

\(\frac{3}{2\cdot6}+\frac{3}{6\cdot10}+\frac{3}{10\cdot14}+...+\frac{3}{26\cdot30}\)

\(=\frac{3\cdot4}{2\cdot6\cdot4}+\frac{3\cdot4}{6\cdot10\cdot4}+\frac{3\cdot4}{10\cdot14\cdot4}+...+\frac{3\cdot4}{26\cdot30\cdot4}\)

\(=\frac{3}{4}\left(\frac{4}{2\cdot6}+\frac{4}{6\cdot10}+\frac{4}{10\cdot14}+...+\frac{4}{26\cdot30}\right)\)

\(=\frac{3}{4}\cdot\left(\frac{1}{2}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+\frac{1}{10}-\frac{1}{14}+...+\frac{1}{26}-\frac{1}{30}\right)\)

\(=\frac{3}{4}\cdot\left(\frac{1}{2}-\frac{1}{30}\right)\)

\(=\frac{3}{4}\cdot\left(\frac{15}{30}-\frac{1}{30}\right)\)

\(=\frac{3}{4}\cdot\frac{7}{15}\)

\(=\frac{7}{20}\)