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Gerald Edgar
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What you easily get for any integer k >= 2$k \ge 2$ is the sum of 1/n^k$\sum 1/n^k$ summed over all nonzero integers n$n$, both positive and negative. When k$k$ is even, we can use this to evaluate zeta(k)$\zeta(k)$. When k$k$ is odd, we get the (correct, but uninteresting) result 0$0$.

What you easily get for any integer k >= 2 is the sum of 1/n^k over all nonzero integers n, both positive and negative. When k is even, we can use this to evaluate zeta(k). When k is odd, we get the (correct, but uninteresting) result 0.

What you easily get for any integer $k \ge 2$ is $\sum 1/n^k$ summed over all nonzero integers $n$, both positive and negative. When $k$ is even, we can use this to evaluate $\zeta(k)$. When $k$ is odd, we get the (correct, but uninteresting) result $0$.

Source Link
Gerald Edgar
  • 41.1k
  • 5
  • 125
  • 219

What you easily get for any integer k >= 2 is the sum of 1/n^k over all nonzero integers n, both positive and negative. When k is even, we can use this to evaluate zeta(k). When k is odd, we get the (correct, but uninteresting) result 0.