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?
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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.
http://mathurl.com/crlxvwc.png
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:
http://i.imgur.com/hkfwhCg.jpg
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.