E. Let s, be a bounded sequence, and let t, converge to L. i. Show that if L = 0, then the product s, · tn also converges to 0. ii. Give an example where s, is bounded and t, converges, but where the...

E. Let s, be a bounded sequence, and let t, converge to L.<br>i. Show that if L = 0, then the product s, · tn also<br>converges to 0.<br>ii. Give an example where s, is bounded and t, converges,<br>but where the product does not converge.<br>Hint: One approach to (i) uses the Sandwich Theorem.<br>

Extracted text: E. Let s, be a bounded sequence, and let t, converge to L. i. Show that if L = 0, then the product s, · tn also converges to 0. ii. Give an example where s, is bounded and t, converges, but where the product does not converge. Hint: One approach to (i) uses the Sandwich Theorem.

Jun 03, 2022

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E. Let s, be a bounded sequence, and let t, converge to L. i. Show that if L = 0, then the product s, · tn also converges to 0. ii. Give an example where s, is bounded and t, converges, but where the...

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