Summing up Series

Given the series:
1/((n+1)(3^(n+1))
Prove that it converges or diverges. If it converges, find its sum.

I can prove that it converges, but how would I find the sum?

You missed the most crucial information.

Ah, from 1 to infinity.

Well, just find the partial sums and then take the limit of it as it approaches infinity.

Figured it out. It wasn't partial sums.

-ln(1 - x) = sum from 0 to infinity of (x^(n+1))/(n + 1)
In my case, x = 1/3.
So, the sum is -ln(2/3).

It's -1/3 + ln(3/2)

My work:

What am I missing?

EDIT: It starts at 0, not 1 once I looked over the problem again.

Dat handwriting.

Anyway

If it's zero then it's ln(3/2) but:

-ln(2/3) = -ln(2) - (-ln(3)) = ln(3) - ln(2) = ln(3/2)

So it's the same thing.

Dat handwriting.

Anyway

If it's zero then it's ln(3/2) but:

-ln(2/3) = -ln(2) - (-ln(3)) = ln(3) - ln(2) = ln(3/2)

So it's the same thing.

Late to the party but (-1)*ln(2/3) = ln((2/3)^(-1)) = ln(3/2) is another way to show that.