- #1
janewaybos
- 3
- 0
Homework Statement
Use the definition of convergence to prove that lim n→∞ (1/2)^n=0
The definition of convergence says |a_n-L|<ε
Homework Equations
The Attempt at a Solution
As I understand it:
|(1/2)^n-0|<ε
|(1/2)|^n<ε
then I need to solve for n?
n>(ln(ε))/ln(|1/2|)
Then I choose N=(ln(ε))/ln(|1/2|) but I don't understand why.
n>N>(ln(ε))/ln(|1/2|)??
Given that ε>0 and n>N
then n>(ln(ε))/ln(|1/2|)
then solving for ε I get the statement
|(1/2)|^n<ε
from above. Thanks!