Given a sequence (sn) and given k ϵ ℕ, let (tn) be the sequence defined by tn = sn + k. That is, the terms in (tn) are the same as the terms in (sn) after the first k terms have been skipped. Prove that (tn) converges iff (sn) converges, and if they converge, show that lim tn = lim sn. Thus the convergence of a sequence is not affected by omitting (or changing) a finite number of terms.
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