# Find the radius of convergence r of the series r

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(correct)6.(2 pts) The functionf(x) =8xln(1+x)is represented asa power seriesf(x) =n=0(1 pt) Find the sum ofn=1n(n+1)xn=for<x<.Find the radius of convergenceRof the series.7.(1 pt) The functionf(x) =2x2arctan(x4)is represented asa power seriesf(x) =n=0cnxn.What is the lowest term with a nonzero coefficient.Find the radius of convergenceRof the series.8.(1 pt) A famous sequencefn, called the Fibonacci Se-quence after Leonardo Fibonacci, who introduced it aroundA.D. 1200, is defined by the recursion formulaf1=f2=1,fn+2=fn+1+fn.Find the radius of convergence ofn=1fnxn.Radius of convergence:.9.(1 pt) Find the sum ofn=1n(n+1)xn=for<x<.