Question

Chứng tỏ: S = 1/2² + 1/3² +..............+1/n² < 1 

Answer 1

Ta có:\(\frac{1}{2^2}<\frac{1}{1.2};\frac{1}{3^2}<\frac{1}{2.3};...............;\frac{1}{n^2}<\frac{1}{\left(n-1\right).n}\)

\(\Rightarrow S<\frac{1}{1.2}+\frac{1}{2.3}+...........+\frac{1}{\left(n-1\right).n}\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...........+\frac{1}{n-1}-\frac{1}{n}\)

=\(1-\frac{1}{n}<1\)

Vậy S<1

Answer 2

mún thì 1 k

ko mún thì 50 k