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Determine whether each series is convergent or divergent.
4)Determine whether the series converges or diverges.
5)Determine whether the sequence converges or diverges.
Solution
a)
Looking at the right-hand side of the Riemann zeta-function, we recognizeit to be a p-series with
p = x. We know that p-series only converge when p > 1and that they diverge whenever p <= 1,
so the domain of the Riemann zeta-function is
(1,)={x:x>1}

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Determine whether each series is convergent or divergent..pdf

  • 1. Determine whether each series is convergent or divergent. 4)Determine whether the series converges or diverges. 5)Determine whether the sequence converges or diverges. Solution a) Looking at the right-hand side of the Riemann zeta-function, we recognizeit to be a p-series with p = x. We know that p-series only converge when p > 1and that they diverge whenever p <= 1, so the domain of the Riemann zeta-function is (1,)={x:x>1}