# Thread: convergence question

1. ## convergence question

what law to use
$\displaystyle \frac{k+(-1)^k}{k-(-1)^k}$
to find out if it converges or diverges

2. ## Re: convergence question

Hello, transgalactic!

$\displaystyle \text{Converge or diverge? }\:\lim_{k\to\infty}\frac{k+(-1)^k}{k-(-1)^k}$

$\displaystyle \text{Divide numerator and denominator by }k:$

. . $\displaystyle \lim_{k\to\infty}\frac{1 + \frac{(-1)^k}{k}}{1 - \frac{(-1)^k}{k}} \;=\; \frac{1 + 0}{1 - 0} \;=\;1$

3. ## Re: convergence question

Originally Posted by transgalactic
what law to use
$\displaystyle \frac{k+(-1)^k}{k-(-1)^k}$
to find out if it converges or diverges
is this the kth term of a sequence or a series?