Mathematics, 28.11.2021 14:00, 727

Let f be a real-valued function such that f, f1 , and f^11 are all continuous on [0, 1]. Consider the series P∞

k=1 f( 1 /K

(a) Prove that if the series P∞

k=1 f(1

convergent, then f(0) = 0

>>f^1

(0) = 0.

(b) Conversely, show that if f(0) = f^1

(0) = 0, then the series P∞

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Let f be a real-valued function such that f, f1 , and f^11 are all continuous on [0, 1]. Consider...