5. Let {an1 be a sequence. (a) Prove that limnan = L if and only if limno (an - L) = 0. (b) Prove that limn→∞ an = 0 if

[answerhappygod]

5 Let An1 Be A Sequence A Prove That Limnan L If And Only If Limno An L 0 B Prove That Limn An 0 If 1 (17.5 KiB) Viewed 33 times

5. Let {an1 be a sequence. (a) Prove that limnan = L if and only if limno (an - L) = 0. (b) Prove that limn→∞ an = 0 if and only if limn→∞ |an| = 0. (c) Prove that if limn→∞ an = L, then limn→∞ |an| = |L|.