Calculus Lab Question.... need your help in checking my answer

[Sorc.Polgara]

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

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

I came up with a summation in Sigma Notation to represent this:

k         1   
∑  ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
i=1        i - 1
        2·3

In my notes I have Sigma Notation expressed:

n
∑   a(i)
i=m

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:

      1   
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
      k - 1
2·3

??

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

[Rule]

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?

[Sorc.Polgara]

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?

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?

[Rule]

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).