Question

Limits Help

Answer 1

Limn n->infinity a^n for a E R

Answer 2

I think that would be infinity right?

Answer 3

\[if~\left| a \right|<1,then~\lim_{n \rightarrow \infty}a^n=0\]
\[if~a~\le -1,then~\lim_{n \rightarrow \infty }=-\infty ,if ~a \ge1,then~\lim_{n \rightarrow \infty}a^n=\infty \]

Answer 4

however when a<0 , the signs alternate so limit really doesn't exist or is indeterminate

Answer 5

Thank you, I assumed it was infinity but you have made it a lot easier to understand :)
I have another limit question I could use your help on if you don't mind? I really struggle with limits :S

Answer 6

\[\lim_{n \rightarrow \infty} \frac{ (a-1)^{n} }{ a ^{(n-1)} } a \ge 1\]

Answer 7

lets rewrite this
\[\frac{(a-1)^n}{\frac{a^n}{a}}\]

Answer 8

\[= a* \frac{(a-1)^n}{a^n}\]
\[= a*(\frac{a-1}{a})^n\]

Answer 9

now you have a fraction less than 1
\[\lim_{n \rightarrow \infty} r^n = 0 , r <1\]

Answer 10

so the limit tends towards 0 because the fraction is less than 1 :D

Answer 11

yep :)

Answer 12

wow, so simple in reality, I just hate how the questions are worded :S thank you for your help! :)

Answer 13

yw