Try a partial fraction decomposition.
and
and .
Therefore .
So
.
Clearly this sum is convergent and converges to .
It's the sum from n=1 to infinity of 4/(n^2+2n).
Shouldn't this be converging to 0? I don't understand how to work this out and I have my midterm tomorrow. It says it converges to 3 but I don't understand how it gets there. What convergence test do I use?
Hello, Reefer!
Shouldn't this be converging to 0?
No, the terms are getting smaller and converge to 0,
but they are asking about the sum of the terms.
It says it converges to 3, but I don't understand how it gets there.
We have: .
Partial Fraction Decomposition
We have: .
Multiply through by
. . Let
. . Let
Hence: .
Then: .
Write out the infinite sum:
We see that all the fractions cancel out except and
So we have: .
. .Therefore: .
The sum obviously doesn't converge to 0 since it is a sum of positive numbers!
couldn't possibly be 0!
Are you confusing the series (sum) with the sequence? In order that a series converge, the sequence of values must converge to 0.
I don't understand how to work this out and I have my midterm tomorrow. It says it converges to 3 but I don't understand how it gets there. What convergence test do I use?