Let S = {r: r is a positive number such that ork/k! converges absolutely for ||

Question

Let S = {r: r is a positive number such that ork/k! converges absolutely for || <r
}. Which of the following statement is true?
(a) S is empty.
(b) S is nonempty and r ≤ 1 for all r € S.
(c) S is nonempty and if for some r € S, a function f is defined as
f(x) = Σ
k=0
k!
for x = (-r, r), then f'(x) > f(x) for x = (0,r).
(d) S = (0, ∞0).
(c) None of the above statements is true.

Kunduz · Accepted Answer

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