Answer:
To calculate [tex]r[/tex], calculate the quotient of two consecutive terms.
[tex]r = \frac{\frac{2(n+1)!}{2^{2(n+1)}}}{\frac{2n!}{2^{2n}}}= \frac{n+1}{4}[/tex]
For all [tex]n \ge 4[/tex], [tex]r>1[/tex], so the series converges, as the series grows (even more than) exponentially.
