Question

1) So sánh \(A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{300^2}\) với \(\frac{3}{4}\).

2) Chứng minh rằng :  \(B=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}<1\).

3) Chứng minh rằng : \(C=\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{99}>1\).

4) Tìm x, biết : 70 : \(\frac{4x+720}{x}=\frac{1}{2}\).

 

Answer 1

1/3^2 < 1/2.3

1/4^2 < 1/3.4

.... 

1/300^2 < 1/299.300

=> A < 1/2^2 + 1/2.3 + 1/3.4 + ... + 1/299.300

A < 1/4 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/299 - 1/300

A< 1/4 + 1/2 - 1/300

A< (1/4 + 1/2) - 1/300

A< 3/4 - 1/300 <3/4