Question

Find the radius of Convergence and Interval of Convergence for the given power series

Answer 1

\[\sum_{n=1}^\infty \frac{2^n}{n}x^n\]

Answer 2

\[a_n=\frac{2^n}{n}\]

\[a_{n+1}=\frac{2^{n+1}}{n+1}\]

Answer 3

i guess |x| >= 1/2

Answer 4

\[|(x-0)|\lim_{n-> \infty} |\frac{\frac{2^n}{n}}{\frac{2^{n+1}}{n+1}}|\]

Answer 5

\[|x-0| \lim_{n->\infty}|\frac{2^n}{n}*\frac{n+1}{2^{n+1}}|\]

Answer 6

\[|x-0|\lim_{n->\infty}|\frac{2^n}{n}*\frac{n+1}{2^n*2}\]

Answer 7

i think you're right