1. Determine whether the following series converge. Rigorously justify your answers (using the convergence tests from the lecture). (a) n=1 Ξ M8 M8 (8) Σ Σ n=1 η n2 + 1’ η2 n4 + 1 n! (2η)!’ (b) 00 n=1 2n n! (e) Σ(-1)n+1 n=1 η (h) ΣΙΣ n=0 \m=0 2m 1 3η + 2’ (c) 00 n=0 00 2n 1 + 2n' n=1 (f) Σ(-1)n+1 (-1)^+1/sinn

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