What test would you use to find if the following infinite series converges:
Starting at k=1 ((k)!^2) 2^k/(2k+2)! That is k factorial squared times 2 to the k divided by 2k+2 factorial.
Cheers,
David
Ratio test seems to work fine:
$\displaystyle \lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right| = \lim_{n \to \infty} \left| a_{n+1} \cdot \frac{1}{a_n}\right| = \lim_{n \to \infty} \left| \frac{\left[(n+1)!\right]^2 \cdot 2^{n+1}}{\left(2(n+1)+2\right)!} \cdot \frac{(2n+2)!}{(n!)^2 \cdot 2^n}\right| = \cdots$