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The back of my book says it converges, but each test I've tried says the summation diverges. Can someone help me to know if the following converges?

$$\sum_{n=1}^\infty (n+1)\left(\frac{(1+\sin(nπ/6))}{3}\right)^n $$

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    Yes, please try Wolfram Alpha (very large number, but converges) - maybe try the Cauchy root test to show.2012-09-21

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