Given xn = [1 + (- 1) ^ n] / n how to prove his limit is 0 by definition

Given xn = [1 + (- 1) ^ n] / n how to prove his limit is 0 by definition

|Xn-0|=[1+(-1)^n]/n≤2/n
For any given positive number, let | xn-0 | ε, as long as 2 / N | ε, that is, n | 2 / ε. Take the positive integer n = [2 / ε], when n | xn-0 | ε
So LIM (n →∞) xn = 0
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[x] It's a rounding function