zorro
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What is wrong?
dextercioby said:I hope the OP sees that nothing in his limit diverges so would it need to be <reingeneered> ??
CompuChip said:Nothing's wrong, the fact that you can rewrite the function such that the limit becomes of the form 'infinity/infinity' when evaluated 'naively' does not mean that the limit suddenly no longer exists. In fact, this is one of the cases where we are allowed to apply L'Hopitals rule, and we then often find a finite answer.
What you could also do, of course, is rewrite it as
\lim_{n \to \infty} \frac{1 + x^n}{1 + x^n} - \frac{2 x^n}{1 + x^n}
and then divide numerator and denominator of the second term by xn (or you can still do that first and then do the same rewriting trick, it just looks a little different).