# 009C Sample Midterm 3, Problem 2

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For each the following series find the sum, if it converges.

If you think it diverges, explain why.

(a)  ${\displaystyle {\frac {1}{2}}-{\frac {1}{2\cdot 3}}+{\frac {1}{2\cdot 3^{2}}}-{\frac {1}{2\cdot 3^{3}}}+{\frac {1}{2\cdot 3^{4}}}-{\frac {1}{2\cdot 3^{5}}}+\cdots }$

(b)  ${\displaystyle \sum _{n=1}^{\infty }\,{\frac {3}{(2n-1)(2n+1)}}}$