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Math Help - convergent or divergent?

  1. #1
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    convergent or divergent?

    Hi, I was wondering if someone can help me with this problem.

    Determine whether the series is convergent or divergent
    \sum_{n=1}^ (infinity) 4 + (3^n) / (2^n)

    Thank you to anyone who can help.
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  2. #2
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    Quote Originally Posted by Wintaker99 View Post
    Hi, I was wondering if someone can help me with this problem.

    Determine whether the series is convergent or divergent
    \sum_{n=1}^ (infinity) 4 + (3^n) / (2^n)

    Thank you to anyone who can help.
    Divergent:

    \sum (n=1 to infinity) [4 + 3^n] / (2^n) = \sum (n=1 to infinity) 4/ (2^n) + \sum (n=1 to infinity) 3^n / 2^n

    ................= \sum (n=1 to infinity) 4/ (2^n) + \sum (n=1 to infinity) (3/2)^n

    The first of the sums in the above converges as its a geometric series with factor <1, while the second sum diverges as again it is a geometric series with factor >1.

    RonL
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