Friday, February 12, 2016

calculus - Alternative way to prove limntoinftyfrac2nn!=0?




It follows easily from the convergence of n=02nn! that

limn2nn!=0


Other than the Stirling's formula, are there any "easy" alternatives to show (1)?


Answer



Yes: note that
02nn!2(23)n2


for n3, and then use the squeeze theorem.


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