Question

What would happen if I raised a negative number to power infinity (-x)^∞

Answer 1

\[ (-1)^{\infty} x^{\infty} \]

Answer 2

That is a very good question. Hmm.

Answer 3

So what is (-1)^(infinity)?? how do we know if infinity is even or odd? It's undefined. So, the no. itself is undefined, I guess.

Answer 4

it is undefined ... either -inf or +inf (if |x|>1)
if |x|=1, that would be +1 or -1
if |x|<1. that would be zero

Answer 5

Okay, I guess I have to use the squeeze theorem after all :( The sequence is 10+(-1/9)^infinity, have to figure out the limit or if it diverges.

Answer 6

if |x|<1, x^inf = 0 (or, x^a -> 0, a->inf)

Answer 7

Yah that's what I got, the limit tends to 10 as N->infinity. Thanks!