Problem 1698 (difficulty: 5/10)

\(\displaystyle \qquad\sum_{k=1}^\infty\frac1{k^4}=? \qquad \qquad\sum_{k=1}^\infty\frac1{k^2-\frac14}=? \qquad \qquad\sum_{k=1}^\infty\frac1{k^2+1}=? \)

Give me another random problem!