\(A=\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+...+\dfrac{1}{13\times15}\)
\(2A=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{13}-\dfrac{1}{15}\)
\(2A=\dfrac{1}{1}-\dfrac{1}{15}\)
\(2A=\dfrac{14}{15}\)
\(A=\dfrac{7}{15}\)
\(A=\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+\dfrac{1}{5\cdot7}+...+\dfrac{1}{13\cdot15}\)
\(\Rightarrow2A=\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{13\cdot15}\)
\(\Rightarrow2A=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{13}-\dfrac{1}{15}\)
\(\Rightarrow2A=1-\dfrac{1}{15}\)
\(\Rightarrow A=-\dfrac{1}{14}:2\)
\(\Rightarrow A=-\dfrac{1}{28}\)
Mình sửa lại tí nhé:
\(\Rightarrow2A=\dfrac{14}{15}\)
\(\Rightarrow A=\dfrac{14}{15}:2\)
\(\Rightarrow A=\dfrac{7}{15}\)
