Question

Tính tổng 50 số hạng đầu tiên của dãy: \(\dfrac{1}{2.4};\dfrac{1}{4.6};\dfrac{1}{6.8}\)

Answer 1

\(\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{48.50}\)

\(\Leftrightarrow\dfrac{1}{2}\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{48.50}\right)\)

\(\Leftrightarrow\dfrac{1}{2}\left(\dfrac{4-2}{2.4}+\dfrac{6-4}{4.6}+...+\dfrac{50-48}{48.50}\right)\)

\(\Leftrightarrow\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+..+\dfrac{1}{48}-\dfrac{1}{50}\right)\)

\(\Leftrightarrow\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{50}\right)\)

\(\Leftrightarrow\dfrac{1}{2}.\dfrac{24}{50}=\dfrac{6}{25}\)