7. Let {bk} be a real sequence and bE R. (a) Suppose that there is an N...
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7. Let {bk} be a real sequence and bE R.
(a) Suppose that there is an N E N such that I b - bk I :::; M for all k 2: N. Prove that n N nb - 2: bk :::; 2: Ibk - bl + M(n - N)
k=l k=l for all n > N.
(b) Prove that if bk ~ bask ~ 00, then as n ~ 00.
(c) Show that the converse of
(b) is false.
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