Question

[ミ★ℒїøŋεℓ Ɱεşşї★彡 (Team Football P...]

A=24/1.3.5+24/3.5.7+24/5.7.9+...+24/25.27.29

Answer 1

[Đoàn Đức Hà]

\(A=\frac{24}{1.3.5}+\frac{24}{3.5.7}+\frac{24}{5.7.9}+...+\frac{24}{25.27.29}\)

\(A=6\left(\frac{4}{1.3.5}+\frac{4}{3.5.7}+\frac{4}{5.7.9}+...+\frac{4}{25.27.29}\right)\)

\(A=6\left(\frac{5-1}{1.3.5}+\frac{7-3}{3.5.7}+\frac{9-5}{5.7.9}+...+\frac{29-25}{25.27.29}\right)\)

\(A=6\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{25.27}-\frac{1}{27.29}\right)\)

\(A=6\left(\frac{1}{1.3}-\frac{1}{27.29}\right)=\frac{520}{261}\)