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Math Help - series question

  1. #1
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    series question

    Hey guys I can't seem to get the answer for this so thanks if anybody could help:

    The rth term of a series is 3^(r-1)+2r. Find the sum of the first n terms.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by margaritas View Post
    Hey guys I can't seem to get the answer for this so thanks if anybody could help:

    The rth term of a series is 3^(r-1)+2r. Find the sum of the first n terms.
    \sum_{r=1}^{ n} 3^{r-1}+2r = \left( \sum_{r=1}^{ n} 3^{r-1} \right)+ \left( \sum_{r=1}^{ n} 2r \right)

    The first of these is a finite geometric series which you should be able to sum
    and the second is a finite arithmetic series which you should also be able to sum

    RonL
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  3. #3
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    No, actually I still don't get it. Could you elaborate further? Thanks!

    EDIT: Oh no wait, I think I get it!
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  4. #4
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    Quote Originally Posted by margaritas View Post
    No, actually I still don't get it. Could you elaborate further? Thanks!

    EDIT: Oh no wait, I think I get it!
    For the record:
    \sum_{k = 0}^n ar^k = \frac{a(1 - r^{n+1})}{1 - r}

    and

    \sum_{k = 0}^n k = \frac{n(n+1)}{2}

    and you can take it from there.

    -Dan
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  5. #5
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    Quote Originally Posted by margaritas View Post
    No, actually I still don't get it. Could you elaborate further? Thanks!

    EDIT: Oh no wait, I think I get it!
    <br />
\sum_{r=1}^{ n} 3^{r-1} = \frac{1-3^r}{1-3}<br />

     \sum_{r=1}^{ n} 2r = r(r+1)

    RonL
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