101Views4Replies

Author Options:

Does anyone want a really enjoyable Maths problem I've been thinking about for days? Answered

Here is it:
Prove that (Xn): (any) n Xn=1+1/1!+1/2!+1/3!.....+1/n! converges and lim(Xn)=lim(Yn), where
                    n
Yn=(1+1/n)

( (any) is upside down A, n in the end is power)
I know asking homework-based questions is unethical, but I've been doing it for 2 weeks and my teacher tells me it is very enjoyable...

Any ideas?

4 Replies

user
kelseymh (author)2010-10-13

I'm not a good enough mathematician to see why the Bolzano-Weierstrass existence theorem applies in this particular case.

All I could do is to churn through the math; in particular doing the expansion of Yn and showing that it's the same as the sum of inverse factorials term by term. Brute force is never elegant :-(

Asking homework-based problems is frowned upon around here only if you don't disclose it. You haven't done that, and you've given the background that this isn't just "ooh, I need an answer for tomorrow's exam." :-) I for one am interested to see what our mathematician members come up with...

Select as Best AnswerUndo Best Answer

user

Sometimes you guys frighten me.

Select as Best AnswerUndo Best Answer

user
gruffalo child (author)kelseymh2010-10-14

The problem was almost right after the Bolzano-Weierstrass theorem in the paper, and as Xn+1=Xn + 1/(n+1)! it is monotonous and rising, and if I prove that (exist) C: (any) n Xn0 than it converges, and sup Xn =lim Xn. Maybe it can help...

Select as Best AnswerUndo Best Answer

user
steveastrouk (author)2010-10-13

Tried an inductive method ?

Select as Best AnswerUndo Best Answer