convergence question

**transgalactic** · July 8th 2011, 01:56 PM

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

**Soroban** · July 8th 2011, 04:47 PM

Hello, transgalactic!

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

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

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

**skeeter** · July 8th 2011, 04:48 PM

Originally Posted by transgalactic

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

is this the kth term of a sequence or a series?

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