Question

[Nguyễn Thị Hải Yến]

Cho biểu thức A=1/1.3+1/3.5+1/5.7+...+1/37.39.Hãy so sánh A với 1/2

Answer 1

[Nguyễn Lê Phước Thịnh]

\(A=\dfrac{1}{2}\cdot\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{37\cdot39}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{37}-\dfrac{1}{39}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{38}{39}< \dfrac{1}{2}\)