Here's something of interest. I've always learned that \(\displaystyle \lim_{n \to \infty} 1^n\) is indeterminate.

(I also looked it up and the wikipedia article agreed with me, anyway.) But W|A says it's 1. Strange.

-Dan

@ Debsta

@ topsquark

It (the form) is indeterminate. Please look at these examples after you put them into graphing/other calculators and/or computers:

limit as n ---> oo \(\displaystyle \ \) of \(\displaystyle \ \bigg(1 \ + \ \dfrac{1}{n^2}\bigg)^n\)

limit as n ---> oo \(\displaystyle \ \) of \(\displaystyle \ \bigg(1 \ + \ \dfrac{1}{n^2}\bigg)^{n^2}\)

limit as n ---> oo \(\displaystyle \ \) of \(\displaystyle \ \bigg(1 \ + \ \dfrac{1}{n^2}\bigg)^{n^3}\)

limit as n ---> oo \(\displaystyle \ \) of \(\displaystyle \ \bigg(1 \ - \ \dfrac{1}{n^2}\bigg)^n\)

limit as n ---> oo \(\displaystyle \ \) of \(\displaystyle \ \bigg(1 \ - \ \dfrac{1}{n^2}\bigg)^{n^2}\)

limit as n ---> oo \(\displaystyle \ \) of \(\displaystyle \ \bigg(1 \ - \ \dfrac{1}{n^2}\bigg)^{n^3}\)

There should be at least four different limit values from the above. I haven't checked them all.

(Edit) For similar reasons, the form in # 8 is also indeterminate.