The Calculus Lab assignment is covering Sigma Notation.  Here is the problem I'm having trouble with:

[quote]
2.  Find the kth term of the sum 1/2 + 1/6 + 1/18 + 1/54 + ....
[/quote]

I came up with a summation in Sigma Notation to represent this:
[quote]
k        1   
∑  ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
i=1        i - 1
        2·3
[/quote]

In my notes I have Sigma Notation expressed:
[quote]
n
∑  a(i)
i=m
[/quote]
with the "a(i)" part labeled as the "terms"...

NOTE:  "a(i)" really is suppose to be "a" with a subscript of "i", I just don't know how to do this in a post.

So would the kth term be:
[quote]
      1   
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
      k - 1
2·3
[/quote]

????????

I have this feeling that I might be wrong.  If anyone could help, I'd greatly appreciate it.

If you want to label what comes first the "zeroth" term the answer is
1/2 * (1/3)^k 

If you want k=1 to be the first term,
1/2 * (1/3)^(k-1)


The series is

Sum[k=1, k=infinity ]  1/2 * (1/3)^(k-1)

It was too straining to look at the formatting in your quotes, so is this what you thought?

[quote author=Rule link=topic=14813.msg150949#msg150949 date=1145576500]
If you want to label what comes first the "zeroth" term the answer is
1/2 * (1/3)^k 

If you want k=1 to be the first term,
1/2 * (1/3)^(k-1)


The series is

Sum[k=1, k=infinity ]  1/2 * (1/3)^(k-1)

It was too straining to look at the formatting in your quotes, so is this what you thought?

[/quote]Yes, that's what I'm trying to write in my quotes.

So... is my answer "1/2 * (1/3)^(k-1)" correct or are you just trying to verify what I was trying to say?

Yes that's correct.  I didn't really look at what you were trying to say, because it wasn't pretty :).  (At least, it doesn't format properly for me).