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This assignment will count the same as a WeBWorK homework and is due 11/8 at the beginning of class. I expect clear thinking with COMPLETE sentences and proper grammar. Typing is not required, but nice handwriting is appreciated. 1. 2. (5 points) Suppose that lim nan = 1. Prove that n→∞ (5 points) Prove that if ∞ P ∞ P an diverges. n=1 an is a convergent series of positive terms then n=1 (5 points) Prove that if an > 0 and lim (an )1/n = R then diverges if R > 1. n→∞ ln(1 + an ) n=1 converges. [Hint: consider the function f (x) = x − ln(1 + x)] 3. ∞ P ∞ P n=1 an converges if R < 1 and