n is natural, and n->+inf.
The problem is you can't separate the expression and calculate the product of both limits...
Hmmmmm....
That's the same "error" that TD pointed out (if error it is). And it appears I lied... The expression with n = 1000 (as far as my calculator will go) appears to be decreasing but fairly flat (first derivative at n = 1000 is -2 x 10^(-7)) and only at 0.6 or so.
I can't say why TPH and Soroban's methods would be wrong, but I don't think the answer is 1.
-Dan
You seem to be right, I graphed it too.
However, I am confused why my results produced the incorrect answer. It is certainly that the limit composition rule failed, for some reason. Perhaps, when I said it works for was wrong, I know that it works for numbers, I just always assumed it works for infinite limits also. Apparently it seems by assumption was wrong.
Though I can prepared to be wrong, and think I am. What you shown was not a proof . It needs to be formal.
EDIT. I realized my mistake.
What I said about composition functions holds true. But I have not properly expressed the outer function, I assumed it was raised to the , but that does not succesfully express the outer function.
I was also thinking about using a series expansion on this one, but I think you made it as simple as possible. Good job.
It looks correct to me. Again as I said the limit composition rule is used here.
The only think I am concerned about is whether a distribution of the limit to each individual term is allowed in an infinite series. I think yes, I believe you can always do it. Or whether the series need to be absolutely convergent, but I think you are correct about this one.
Not to offend you but I realized that in my engineering class. The professor just manipulates that stuff and differencials in an way he wants to.
It some ways I agree with that approach. I think I am the only mathemation in my differencial equations class. I have made some remarks about the professors' solution after class, he told me he would be concered with it if he was in a roomful of mathemations but engineers do not need to know that stuff. In fact, If I want to for example, differencial equations on a serious level I would first learn how to solve them informally and incorrectly. Then I would learn the theory, so that I not have to memorize techniques to how to solve them, that stuff I would already know and only be concerned with about the theory.