Question $18$

Consider the power series ${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^n\frac{1}{n*4^n}(x-1{)}^n.$

Answer each part below. Put your answers directly $in$ the text box,

clearly labeling each part $of$ the problem with the part number. You

may use the equation editor $if$ you wish, but this $is$ not required.

Part $1(4$ points$).$ Find the radius $of$ convergence for the series.

Part $2(5$ points$).$ Find the interval $of$ convergence for the series. $If$

your interval has endpoints, you should determine whether $or$ not

each end point should, $or$ should not, $be$ included $in$ the interval.