Determine the convergence of ∑n=1∞n50n!\sum_{n=1}^{\infty} \frac{n^{50}}{n!}∑n=1∞n!n50. Which analysis is correct?
By Ratio Test, limn→∞an+1an=0<1\lim_{n \to \infty} \frac{a_{n+1}}{a_n} = 0 < 1limn→∞anan+1=0<1; series converges
The factorial in the denominator grows faster than any polynomial; heuristically converges
By Direct Comparison to ∑1n2\sum \frac{1}{n^2}∑n21; series converges
All of A, B, and C are valid reasoning