Using the definition prove the convergence of the following sequences:
(i) lim Cos nα
n+1
= 0 (ii) lim n
3−1
3+2n3 =
1
2
(iii) lim 1
(n+1)
2 +1
=0
Further, find all x∈ ℝ that satisfy the inequality: |x|+ |x + 1|<2
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