Converging and diverging Series

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Homework Statement
Deduce whether these three series are converging or diverging
Relevant Equations
Convergence tests
Would somebody be kind enough to check whether I've picked the right convergence tests for each of these and reached the right answers? There are no solutions in the book.

Also, is there a method I can use to determine if I'm right - does calculating the first n terms help?

Thank you
Edit: meant to say it's for all integers one and over. Plus, the denominator in question 1 is meant to read 3n-2.
 

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Here's corrected question 1
 

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penroseandpaper said:
Homework Statement:: Deduce whether these three series are converging or diverging
Relevant Equations:: Convergence tests

Would somebody be kind enough to check whether I've picked the right convergence tests for each of these and reached the right answers? There are no solutions in the book.
Your work looks fine to me (including the edited version of question 1). Sometimes there are multiple convergence tests that work, so there might not be only one way to determine whether a sequence converges.
penroseandpaper said:
Also, is there a method I can use to determine if I'm right - does calculating the first n terms help?
For some sequences, calculating the first n terms doesn't help. For example, ##s_n = \{ (-1)^n\}, n \ge 1##.
penroseandpaper said:
Thank you
Edit: meant to say it's for all integers one and over. Plus, the denominator in question 1 is meant to read 3n-2.
 
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