Answer to Question #208696 in Real Analysis for AGRAHARAPU VEERAVA

Question

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