How does one prove that Σ(2n)!!/(2n+1)!! diverges? The ratio test is inconclusive and I don't know how to use the comparison test and the limit comparison test in the situation.
Edit: I found an answer to my question here.
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What is your definition of double factorial? – Arthur Nov 15 '16 at 20:29
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Do you know Raabe's test? – Daniel Fischer Nov 15 '16 at 20:30
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(2n) = 2 · 4 · 6 ·...· 2n and (2n + 1) = 3 · 5 · 7 ·...· 2n + 1 – David Nov 15 '16 at 20:31
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No I haven't heard of Raabe's test but I'll look it up. – David Nov 15 '16 at 20:31
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1You could also work with Stirling's formula, converting double factorials into expressions with factorials isn't too hard. – Daniel Fischer Nov 15 '16 at 20:32