a. Show that if two power series E-oa„x" and E-o b,x" are convergent and equal for all values of x in an open interval (-c, c), then a, = b, for every n. (Hint: Let f(x) = E0a,x" = show that a, and b, both equal f®(0)/(n!).) b. Show that if Eo a,x" = 0 for all x in an open interval (-c, c) then a,n E=ob,x". Differentiate term by term to 0 for every n.

Q: can anything be said about E- an

A: Given that, ∑nan converges.

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