Question

Cho tổng : A=1/2x2+1/3x3+1/4x4+...+1/100x100. Chứng tỏ A<25/26

Answer 1

A= \(\frac{1}{2.2}+\frac{1}{3.3}+\frac{1}{4.4}+...+\frac{1}{100.100}< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}=1-\frac{1}{100}=\frac{99}{100}\)

=> A= \(\frac{99}{100}>\frac{25}{26}\)