# Thread: limits and converges or diverges.

1. ## limits and converges or diverges.

Hello,
plz try to solve these question.

2. Originally Posted by m777
Hello,
plz try to solve these question.
Question 1:

Find the limit: $\lim_{x \to 3} \frac{(x-3)}{3x^2-13x+12}$

Factorise the denominator:

$\lim_{x \to 3} \frac{(x-3)}{3x^2-13x+12}=\lim_{x \to 3} \frac{(x-3)}{(x-3)(3x-4)}=\lim_{x \to 3} \frac{1}{3x-4}=1/5$

Question 2:

Determine if the following series converges or diverges:

$\sum_1^{\infty}4^{k-1}$

As an absolute minimum requirement for convergence of a series, the
terms must go to zero as the sumation index goes to infinity. This series
fails this most basic requirement and thus diverges.

RonL