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Problem 1. Let {Xn} be a sequence of complex numbers which converges to some point X. Prove Problem 2. Let A1,A2,...,An be real numbers. (a). Show that + an (b). Show that + an () Problem 3. Here are two representations for sin(x): where II denotes the infinite product, and Use these facts to prove that n=1 Problem 4. Let A1, A2,..., an be positive real numbers. The Arithmetic-Geometric Mean inequality states that Prove this inequality in the special case that n = 8. (Your answer should utilize Cauchy-Schwarz inequality and should not involve multiplying out terms)

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