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Exercise 2. Consider the sequence (In)n> defined by cos(k) cos(1) cos(2), 2 cos(n) +...+ 2k + n2+1+ m2 2 + m2 n+ n2 (a) Use t

2.

Exercise 2. Consider the sequence (xn)n≥1 defined by xn = Xn k=1 cos(k) k + n2 = cos(1) 1 + n2 + cos(2) 2 + n2 + · · · + cos(n) n + n2 . (a) Use the triangle inequality to prove that |xn| ≤ n 1 + n2 for all n ≥ 1. (b) Use (a) and the -definition of limit to show that limn→∞ xn = 0.

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2. Exercise 2. Consider the sequence (xn)n≥1 defined by xn = Xn k=1 cos(k) k +...
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