Find limit superior and limit inferior for the sequence (an)n∈N=((1/n)+(-1)^n)n∈N
1
Expert's answer
2021-01-29T05:10:57-0500
{an}={n1+(−1)n}
∣an∣=∣n1+(−1)n∣≤2 for all integers n≥1. Hence {an} is bounded.
The first few terms are {0,23,3−2,45,5−4,67,⋯}. The subsequence {a2n}={23,45,67,⋯} converges to 1 and the subsequence {a2n−1}={0,3−2,3−4,⋯} converges to -1. Hence S={−1,1}
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