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- Show that if (sn,tn) converges to (s,t) in ℝ2 with the usual d2 metric, then the sequence converges to the same limit in the d0 ("max") metric.Using the appropriate approach covered in unit 6 of this course along with knowledge gained in unit 1 and 2, verify whether the limit to infinity of n(n + 1)(n + 2)-1 (n + 3)-1 is equal to one.1. Use the definition of the limit ( epsolon - delta ) to show thatlim of 1/z as z approaches -i2. Give the condition which ensure that |ez| < 1 where z in C.
- Show that if (sn,tn) converges to (s,t) in ℝ2 with the d0 ("max") metric, then the sequence converges to the same limit in the usual d2 metric.Using the appropriate approached covered in Unit 6 of this course along with knowledge gained in Unit 1 and 2, verify whether the limit to infinity of n (n +1) (n + 2)-1 (n+3) -1 is equal to one.1. Consider the sequence Xn = √n + 1 − √n, n ≥ 1. Prove that (xn)n isconvergent. Find its limit.