- #1
talk2glenn
Homework Statement
Decide whether the series below is absolutely convergent, conditionally convergent, or divergent:
[tex]\sum_{1}^{\infty}(2n+3)!/(n!)^2[/tex]
The Attempt at a Solution
By graphing the equation, I am confident that the series is divergent, but I don't know how to prove it. I cannot do the algebraic manipulation for a ratio test, assuming it is even possible, and none of the other tests seem applicable. Since it's apparently going to be divergent, I can't to a comparison test.
That leaves either a straight limit test, or a limit comparison test. Unfortunately, it looks to me like the limit converges to zero. Factorial is stronger than the power function, but how can I prove factorial squared is weaker than a larger factorial in the numerator?
Thanks :)