Thursday, December 29, 2016

calculus - Alternative way to prove limntoinftyfrac2nn!=0?


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.


No comments:

Post a Comment

analysis - Injection, making bijection

I have injection f \colon A \rightarrow B and I want to get bijection. Can I just resting codomain to f(A)? I know that every function i...