My instinct is to use the root test, and try to show thatProve that
converges.
.
But unfortunately I don't know how to show this either.
Are there any tricks I can use on these nth root proofs which might help here?
Thanks!
My instinct is to use the root test, and try to show thatProve that
converges.
.
But unfortunately I don't know how to show this either.
Are there any tricks I can use on these nth root proofs which might help here?
Thanks!
Thank you very much, but I could still benefit from further assistance.
Once we have , the proof is easy for me. However, I am uncertain how you arrived at that inequality.
We have by definition
.
I have no idea how to prove that this series is increasing, but let's say for a moment that I could. In that case, we have, for each ,
.
Then algebraically we can show that
flipping:
.
Substitute back to get
,
and expand:
.
But this isn't good enough to get to our goal, which, again, is:
.
Apparently I need to learn more about exponents. Any more tricks would be much appreciated.