It looks to me like the nth term of the series is
[product from k = 1 to n of 2k]/{(2n+2) * [product from k = 1 to n of 2k +1]}
The nth term converges to 0 so it is possible for the series to converge, but I am not sure how to check for convergence of the series.
I hope this helps. I am sorry I am not able to give you a complete answer.
Tyler B.
I attempted this problem by saying since the value of each succeeding term is lower than it's preceding term, the term number infinity would be zero, making the series convegent.
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08/10/18
Paul M.
tutor
That isn't good enough!
The series 1 + 1/2 + 1/3 + … + 1/n diverges despite being a decreasing term series.
The ratio test says that if |an+1/an| converges to L< 1, then the series converges; if the ratio converges to L > 1 or blows up, then the series diverges. I think in this problem the ratio actually converges to 0 and, therefore, the series converges...BUT I am a bit rusty on infinite series and am not absolutely sure. Good luck!
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08/10/18
Paul M.
08/10/18