\(a,\frac{1}{n+1}+\frac{1}{n+2}+......+\frac{1}{2n}\)
\(>\frac{1}{2n}+\frac{1}{2n}+.......+\frac{1}{2n}\) có \(n\) số \(\frac{1}{2n}\)
\(=n.\frac{1}{2n}=\frac{1}{2}\)
\(b,\frac{1}{1^2}+\frac{1}{2^2}+......+\frac{1}{n^2}< \frac{1}{1}+\frac{1}{1.2}+........+\frac{1}{\left(n-1\right).n}\)
\(=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.......+\frac{1}{n-1}-\frac{1}{n}\)
\(=2-\frac{1}{n}\)