Hey guys, can you help me with this on please? First one, I need to proof convergence, and the second one is to find the radius of converge.

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The first series in the part A does not necessarily converge. If $\displaystyle a_n = 2 + n$ then $\displaystyle \sum\limits_{n = 1}^\infty {\frac{1}{{a_n }}} = \sum\limits_{n = 1}^\infty {\frac{1}{{2 + n}}} $ diverges.