0
$\begingroup$

Suppose $b_n$ is a sequence $>0$ and $b>0$ where $b_n$ converge to $b$. Suppose $z_n=\log b_n$ and $z=\log b$, prove that $z_n$ converge to $z$. I know the definition of limit but not sure how to satisfy the condition

  • 1
    Do you know that $\log x$ is a **continuous** function defined on $(0,+\infty)$? What do you know about the erlation of convergent sequences and continuous functions?2012-09-22
  • 0
    prove by definition definition, we need to find a $N$ from sequence $z_n$ st the condition satisfies by not sure how to find $N$, the only hints is taht we can find such $N$ from sequence $b_n$2012-09-22
  • 0
    In order to be able to help we have to know the rules of the game. What is your definition of $\log$, and what properties of $\log$ (or of sequences, for that matter) are you allowed to use?2012-09-22

3 Answers 3