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Math Help - Sum of 3^r

  1. #1
    Senior Member Mukilab's Avatar
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    Sum of 3^r

    How would I find the sum of 3^r from r=1 to r=n?

    I honestly have no workings because I don't know how to approach this since I can't split it into 3*(sum[1^r])
    Thank you for your help.
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  2. #2
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    Re: Sum of 3^r

    Quote Originally Posted by Mukilab View Post
    How would I find the sum of 3^r from r=1 to r=n?

    \sum\limits_{k = 1}^n {t^k }  = \frac{{t - t^{n + 1} }}{{1 - t}}
    Thanks from Mukilab
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  3. #3
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    Re: Sum of 3^r

    Quote Originally Posted by Mukilab View Post
    How would I find the sum of 3^r from r=1 to r=n?

    I honestly have no workings because I don't know how to approach this since I can't split it into 3*(sum[1^r])
    Thank you for your help.
    It's a geometric series with \displaystyle \begin{align*} a = 3 \end{align*} and common ratio \displaystyle \begin{align*} \rho = 3 \end{align*}.

    The sum of a finite geometric series can be evaluated using \displaystyle \begin{align*} S_n = \frac{a \left( 1 - \rho ^n \right)}{1 - \rho} \end{align*}.
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