the limit 25

Calculus Level 2

$\lim_{n \to \infty} \frac {2^n + (-1)^n}{2^{n+1}+(-1)^{n+1}} = \ ?$

2 solutions

Dwaipayan Shikari
Jan 3, 2021

$\lim_{n\rightarrow∞ } \frac{2^n +(-1)^n}{2^{n+1}+(-1)^{n+1}}=\lim_{n\rightarrow∞}\frac{1+(-\frac{1}{2})^n}{2-(\frac{1}{2})^n}= \frac{1}{2}$

There is a typo $\lim_{n\to\infty}$

Hana Wehbi - 4 months, 4 weeks ago

why is it 2 - (1/2)^n instead of 2 - (-1/2)^n ?

Mohamed Sobhy - 4 months, 1 week ago

Mr. Penguin Monster
Feb 5, 2021

(-1)^n is ±1 2^n ± 1 = O(2^n) 2^{n+1} ± 1 = O(2^{n+1}) Therefore the limit is 2^n / 2^{n+1}