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1 2 3 P L K LLL Let an be a bounded sequence of complex numbers. Show that for each > 0, the series

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1 2 3 P L K LLL Let an be a bounded sequence of complex numbers. Show that for each > 0, the series ann converges uniformly for Rez >1+. Here we choose the principal branch of n. Solution ann an C, Rez > 1+. Apply Weierstrass M-test, |ann | < n=1 Cn-Rez " = nIte Mn, Mn < Rez 1+E. an converges uniformly for

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