Question

Tính tổng

S=\(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{23.25}\)

Answer 1

\(S=\dfrac{5-3}{5.3}+\dfrac{7-5}{7.5}....+\dfrac{25-23}{23.25}\)

\(S=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{23}-\dfrac{1}{25}\)

\(S=\dfrac{1}{3}-\dfrac{1}{25}=\dfrac{25-3}{3.25}=\dfrac{7}{25}\)

Answer 2

sửa lại nha bạn

\(\dfrac{25-3}{25.3}=\dfrac{22}{75}\)

Answer 3

\(S=\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{23.25}\)

\(S=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{23}-\dfrac{2}{25}\)

\(S=\dfrac{1}{3}-\dfrac{1}{25}\)

\(S=\dfrac{25}{75}-\dfrac{3}{75}\)

\(S=\dfrac{22}{75}\)