# Thread: series limit and convergence

1. ## series limit and convergence

am i correct ? not sure would like a little help please.

got this sequence

an =7-6n/3n+14

i did this:

an =-6n/3n + 1/2

an = -12n/6n + 1

an = 1/n + 2

so for large numbers of n, 1/n converges to 0 and so converges to an = 2

2. Originally Posted by smartcar29
am i correct ? not sure would like a little help please.

got this sequence

an =7-6n/3n+14

i did this:

an =-6n/3n + 1/2

an = -12n/6n + 1

an = 1/n + 2

so for large numbers of n, 1/n converges to 0 and so converges to an = 2
the nth term of the sequence converges to -2

$\lim_{n \to \infty} \frac{7-6n}{3n+14}$

$\lim_{n \to \infty} \frac{\frac{7}{n} -6}{3+ \frac{14}{n}} = \frac{-6}{3} = -2
$

3. Originally Posted by smartcar29
i did this:

an =-6n/3n + 1/2
You can't break up the denominator because there is a sum there, so this is where your argument fails.