Question

Ai giúp mình câu này với:Tính tổng sau:A=24/1.2.3+24/3.4.5+.....+24/19.20.21

 

 

Answer 1

\(A=\frac{24}{1.2.3}+\frac{24}{2.3.4}+....+\frac{24}{19.20.21}\)

\(A=24.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{19.20.21}\right)\)

\(A=12.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+....+\frac{2}{19.20.21}\right)\)

\(A=12.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-....-\frac{1}{20.21}\right)\)

\(A=12.\left(\frac{1}{2}-\frac{1}{420}\right)=12.\frac{209}{420}=\frac{209}{35}\)