Question

[Hồ Thị Trâm Anh]

Cho A=1-1/2+1/3-1/4+1/5-1/6+...+1/49-1/50. Chứng minh rằng: A<5/6

Answer 1

[Nguyễn Ngọc Anh Minh]

\(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{49.50}\)

\(A< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{48.49}\)

\(A< 1-\frac{1}{49}=\frac{48}{49}< \frac{48}{48}< \frac{40}{48}=\frac{5}{6}\)