Question

So sánh :

Tổng 3 + 1/2^2 + 1/3^2 + 1/4^2 + ........... + 1/50^2 với 4

Answer 1

Ta có: \(\frac{1}{2^2}< \frac{1}{1.2};\frac{1}{3^2}< \frac{1}{2.3};...;\frac{1}{50^2}< \frac{1}{49.50}\)

=> \(3+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}< 3+\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}\)

=> \(3+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}< 3+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

=> \(3+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}< 3+1-\frac{1}{50}=4-\frac{1}{50}< 4\)

Vậy \(3+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}< 4\)