It follows easily from the convergence of ∑∞n=02nn! that limn→∞2nn!=0 Other than the Stirling's formula, are there any "easy" alternatives to show (1)?
Answer
Yes: note that 0≤2nn!≤2(23)n−2 for n≥3, and then use the squeeze theorem.
It follows easily from the convergence of ∑∞n=02nn! that limn→∞2nn!=0 Other than the Stirling's formula, are there any "easy" alternatives to show (1)?
Answer
Yes: note that 0≤2nn!≤2(23)n−2 for n≥3, and then use the squeeze theorem.
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