Problem 356 (difficulty: 5/10)
Prove that
\(\displaystyle \sum_{n=1}^{\infty} {1\over n^2}<2.\)
Solution:
\(\displaystyle \frac1{n^2}<\frac1{(n-1)n}\) and \(\displaystyle \sum_{n=2}^{\infty}\frac1{(n-1)n}=1\) (telescopic sum).