math120.e166421.Set3 - 1(1 pt Consider the function...

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1.(1 pt)Consider the function arctan(x/10).Write a partial sum for the power series which represents thisfunction consisting of the first 5 nonzero terms. For example, ifthe series weren=03nx2n, you would write 1+3x2+32x4+x=-1:n=1n-2/3x+87n=n=1(77)nn2/3=n=11n2/3,which diverges as a p-series, as per box 1, p.716. So this end-point is not in the interval.Correct Answers:
8. Also indicate the radius of convergence.
102.(1 pt) Find the interval of convergence for the given powerseries.(1 pt) Represent the function2(1-5x)2as a power seriesf(x) =n=0cnxnc0=c1=c2=c3=c4=
3)The series is convergent:from x =, left end included (Y,N):to x =, right end included (Y,N):Solution:R=.
Whenx=-1:n=1n-2/3x+87n=n=1(77)nn2/3=n=11n2/3,which diverges as a p-series, as per box 1, p.716. So this end-point is not in the interval.Correct Answers:
3.(1 pt) Represent the function2(1-5x)2as a power seriesf(x) =n=0cnxnc0=c1=c2=c3=c4=Find the radius of convergenceR=.