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9-44.

Determine whether each of the following infinite series converges or diverges. Explain each answer briefly. If the series converges, calculate its exact sum.

  1.  

    What is ?

  1.  

    This is a geometric sequence with a ratio of .

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    This is also a geometric sequence. What is the ratio? (See part (b).)

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    This can be written as a telescoping sum: