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What is the inclusion-exclusion principle for 4 sets? Do you know what is PIE for 3 sets? If so, what would you guess the 4 set equation is? Once you have the correct equation, it is pretty easy to prove it, esp if you know a good proof of the 2 set case
calculus - Nice proofs of $\zeta (4) = \frac {\pi^4} {90 . . . I know some nice ways to prove that $\\zeta(2) = \\sum_{n=1}^{\\infty} \\frac{1}{n^2} = \\pi^2 6$ For example, see Robin Chapman's list or the answers to the question "Different methods to compute $\\s