Question

1. Consider the sequences defined as follows.(an) =(12,13,23,14,24,34,15,25,35,45,16,26,36,46,56,17, . . .),(bn) =(n2(−1)n)= (−1,4,−9,16, . . .).(i)...

1. Consider the sequences defined as follows.(an) =(12,13,23,14,24,34,15,25,35,45,16,26,36,46,56,17, . . .),(bn) =(n2(−1)n)= (−1,4,−9,16, . . .).(i) For each sequence, give its lim sup and its lim inf. Show your reasoning; definitions are not required.(ii) For each sequence, determine its set of subsequential limits. Proofs are not required.

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