Question

Can you help me apply the ratio test in this problem http://screencast.com/t/k47izXucGNx

Answer 1

you have

\(\lim\limits_{k \to \infty} \dfrac{(k+1)\left( \dfrac{1}{2} \right)^{k+1}}{k\left( \dfrac{1}{2} \right)^{k} } = \lim\limits_{k \to \infty} \dfrac{(k+1) \times \dfrac{1}{2} }{k}\)

then divide top and bottom by k