Question

find the limits of 1^n and 2^n as n goes to infinity
lim_{n -> ∞}1^n=
lim_{n -> ∞}2^n=

Explanation:

Step1: Analyze $\lim_{n

ightarrow\infty}1^n$
For any real - number $n$, $1^n = 1$. So, $\lim_{n
ightarrow\infty}1^n=1$.

Step2: Analyze $\lim_{n

ightarrow\infty}2^n$
As $n$ increases without bound, the function $y = 2^n$ grows without bound. Mathematically, $\lim_{n
ightarrow\infty}2^n=\infty$.

Answer:

$\lim_{n
ightarrow\infty}1^n = 1$
$\lim_{n
ightarrow\infty}2^n=\infty$