Question

PLEASE HELP!!!! IM SO LOST

Answer 1

Answer:

To calculate $r$, calculate the quotient of two consecutive terms.

$r = \frac{\frac{2(n+1)!}{2^{2(n+1)}}}{\frac{2n!}{2^{2n}}}= \frac{n+1}{4}$

For all $n \ge 4$, $r>1$, so the series converges, as the series grows (even more than) exponentially.