Question

A=\(\frac{3}{1\cdot4}\)+\(\frac{3}{4\cdot7}\)+\(\frac{3}{7\cdot10}\)+\(\frac{3}{10\cdot13}\)+\(\frac{3}{13\cdot16}\)

Answer 1

\(A=\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+\frac{3}{10\cdot13}+\frac{3}{13\cdot16}\)

\(A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\)

\(A=1-\frac{1}{16}=\frac{15}{16}\)

Answer 2

\(\frac{13}{16}\)

Answer 3

\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{16}=1-\frac{1}{16}=\frac{15}{16}\)

Answer 4

\(A=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{16}\)

\(A=\frac{1}{1}-\frac{1}{16}\)

\(A=\frac{15}{16}\)

 Vậy A = \(\frac{15}{16}\)

Answer 5

\(A=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}\)

\(\Rightarrow A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\)

\(\Rightarrow A=1-\frac{1}{16}\)

\(\Rightarrow A=\frac{15}{16}\)