Saturday, January 27, 2018

calculus - How to show that limntoinftyleft(frac(1+frac1n2)n2eright)n=1?




I need to find the limit:
limn((1+1n2)n2e)n
So I know that the limit is 1.
Using Squeeze theorem
?((1+1n2)n2e)n(ee)n 1
What should be instead ? ? Is it possible to solve in another way?
Unfortunately, I can't use L'Hôpital Rule or Series Expansion in this task.


Answer



Note that:



((1+1n2)n2(1+1n2)n2+1)n=(1+1n2)n((1+1n2)n2e)n(ee)n=1




Since:



(1+1n2)n1



By Squeeze Theorem:



limn((1+1n2)n2e)n=1


No comments:

Post a Comment

analysis - Injection, making bijection

I have injection f:AB and I want to get bijection. Can I just resting codomain to f(A)? I know that every function i...