I figured an equation that works for this series but have no idea how to calculate it once I have the sum...none of the rules in our book seem to apply.

http://img48.imageshack.us/img48/7261/9244es7.jpg

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- June 1st 2008, 09:14 PMCrazyLondFind the sum of the convergent series?
I figured an equation that works for this series but have no idea how to calculate it once I have the sum...none of the rules in our book seem to apply.

http://img48.imageshack.us/img48/7261/9244es7.jpg - June 1st 2008, 09:25 PMTheEmptySet
- June 1st 2008, 10:43 PMSoroban
Hello, CrazyLond!

Quote:

Geometric series: first term , common ratio

Its sum is: .

- June 1st 2008, 11:19 PMangel.white
I find it easier to look at these like this:

Looking at that a little bit (you can do the first few a_n if it helps to see, then you will be familiar enough to spot it right off) it should be clear that

And since you want to sum all of them, you get

At which point you have the same geometric series that TheEmptySet and Soroban solved for.