Summation of summation?

• Oct 3rd 2010, 06:14 PM
Summation of summation?
I want to figure out the proper summation to figure out a sum of products:
5
x3
----
15
x3
----
45
x3
----
135
x3
___
...

So if n=0 the result is 5, if n=1 the result is 5+15, if n=2, the result is 5+15+45 and so. Hopefully that makes sense. I'm not quite sure how else to put it. Would the best way be to do something like $\displaystyle \sum_{i=0}^{n}5\sum_{j=0}^{i}3^j$? Or is there some more concise way of putting it? I appreciate any help you guys can offer. Thanks.
• Oct 3rd 2010, 06:42 PM
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Quote:

I want to figure out the proper summation to figure out a sum of products:
5
x3
----
15
x3
----
45
x3
----
135
x3
___
...

So if n=0 the result is 5, if n=1 the result is 5+15, if n=2, the result is 5+15+45 and so. Hopefully that makes sense. I'm not quite sure how else to put it. Would the best way be to do something like $\displaystyle \sum_{i=0}^{n}5\sum_{j=0}^{i}3^j$? Or is there some more concise way of putting it? I appreciate any help you guys can offer. Thanks.

Try

$\displaystyle \displaystyle 5\sum_{i=0}^n3^i$