(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use the definition of convergence to prove that lim n→∞ (1/2)^n=0

The definition of convergence says |a_n-L|<ε

2. Relevant equations

3. 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!

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# Homework Help: Use the definition of convergence to prove that the lim (1/2)^n=0

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