Problem 5 Problem 6 i No counter example Let yn 2 and xn 1 sin n for any n 0 we have yn xn However yn converges to 2 and xn diverges ii No counter example as above xn diverges but yn converges to 2 Problem 7 Note The solution for Problem 7 ii is inaccurate Another way to discuss the convergence is as 1 sin L 1 n lim cos 1 1 lim an lim n sin lim diverges n n n n 1 n n n
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