Question

cho A = 1/2^2 + /3^2 + 1/4^2 + ... + 1/9^2 chưng tỏ 8/9 > A >2/5

Answer 1

Ta có:\(A< \frac{1}{1.2}+\frac{1}{2.3}+......+\frac{1}{8.9}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{8}-\frac{1}{9}=1-\frac{1}{9}=\frac{8}{9}\)

Mặt khác:\(A>\frac{1}{2.3}+\frac{1}{3.4}+.......+\frac{1}{9.10}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{9}-\frac{1}{10}=\frac{1}{2}-\frac{1}{10}=\frac{4}{10}=\frac{2}{5}\)

Vậy \(\frac{8}{9}>A>\frac{2}{5}\)

Answer 2

 Bạn Bảo Bình đúng rồi