Question about series?

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I have done the work so far, and have gotten these answers.

a)

$k=5$

b)

$a_0= 20$

$a_1= -6.6667 $

$a_2= 4$

$a_3= -2.85714285714 $

$a_4= 2.2222$

c)

$3.339$

d)

$0.190$

All my answers seem correct except for d)

Can someone explain how I can get this answer.I was also wondering how do you know how many terms to look for? Or is it usually asked?