It follows easily from the convergence of ∑∞n=02nn! that lim Other than the Stirling's formula, are there any "easy" alternatives to show (1)?
Answer
Yes: note that 0\leq \frac{2^n}{n!}\leq 2\Big(\frac{2}{3}\Big)^{n-2} for n\geq 3, and then use the squeeze theorem.
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