Hello tutors, I need help with this series word problem. I apologize it's long, I would break it up into parts but unfortunately, this uses each previous part as a reference. Please let me know how you can come across this, thank you!

Note that the power series 00 Z(1)"(m1)"=1(x1)+(:v1)2(m1)3+'~ n20 is a geometric series. (a) What is its rst term? What is the ratio 7" between each term and the next one? Based on this, when this series does converge, what does it converge to? (Your answer will be in terms of 3:, and therefore is a function of :13. That is, you will have found the function that this power series represents. Note that the power series given here is centered around :13 = 1, so what you've found is a function f (x), whose Taylor series around a: = 1 is the given series.) (b) Either using the fact that this is a geometric series, or using the Ratio Test, determine the largest open interval on which this power series converges. You can now fill in all the blanks in the following definition of a function f (x): OO f (a) = > (-1)"(x - 1)n = when