Question: (3) Let (fn)neN be a sequence in C(0, 1) and (a)keN a sequence of positive numbers, such that the series E1 9k a converges

(3) Let (fn)neN be a sequence in C(0, 1) and (a)keN a

(3) Let (fn)neN be a sequence in C(0, 1) and (a)keN a sequence of positive numbers, such that the series E1 9k a converges and such that ISk+1 - Sell S ar for all keN. Show that Snta(@) - fn(z) S |fnsk - fall sEas jan for all n, k eN and z (0, 1). Use this to show that C((0, 1]) is complete.

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