Given that "r" is a constant real number, I have a series that goes like this:

$$ r^1 + r^2 + r^3 ... $$

Is there a formula that can tell the sum of the first n elements? So basically a formula for calculating this sum:

$$ \sum_{k=1}^{n} r^k $$

Thanks for any help!


This is the sum of a geometric series, with starting term $r$ and common ratio of $r$ as well.

Now, the general sum of the this series is:

$$S = \frac{1-r^{n+1}}{1-r}$$

A special case is when $|r| < 1$:

$$S = \frac{1}{1-r}$$

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    $\begingroup$ What's the point of posting this for the $N$th time? $\endgroup$ – user147263 Nov 11 '15 at 23:15
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    $\begingroup$ To assist users who can't perform a simple google search $\endgroup$ – Varun Iyer Nov 11 '15 at 23:15
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    $\begingroup$ I tried to google it, but since I had no idea that this was called a geometric series, I couldn't really find anything. Now that I know, I can find the answer myself of course. I just didn't know it was called that. But thanks anyway! $\endgroup$ – adam10603 Nov 11 '15 at 23:18
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    $\begingroup$ @NormalHuman you see the OPs answer. $\endgroup$ – Varun Iyer Nov 11 '15 at 23:20
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    $\begingroup$ My point stands: they can be assisted by marking their question as a duplicate of a canonical question, better than by a hurried two-line answer. $\endgroup$ – user147263 Nov 11 '15 at 23:20

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