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Suppose that {a} and {b} are two sequences of real numbers, and that a → L and n=1 n=1 → L where L & R and L = ± co Let {c} be the 'interlaced' sequence a, b, a, b,... defined by C2m-1 = m² 2m = m a b n=1 Use the definition of limit to show lim c = L. 11 → 00

Suppose that {a} and {b} are two sequences of real numbers, and that a → L and n=1 n=1 → L where L & R and L = ± co Let {c} be the 'interlaced' sequence a, b, a, b,... defined by C2m-1 = m² 2m = m a b n=1 Use the definition of limit to show lim c = L. 11 → 00

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose that {a} and {b} are two sequences of real numbers, and that a → L and n=1 n=1 b → L where L & R and L = ± co Let {} be the 'interlaced' sequence a, b, a, ¹... defined by C2m-1 = am² C2m = bm n=1 Use the definition of limit to show lim c = L. 11 → 00 Definition of limit If X ≤ R, a is a limit point of X, and f: X → R, say that the limit of f on X at a is the number L provided that for every e > 0 there is a 8 > 0 such that f(x) L < € whenever xe X and 0 < |ax| < 8.
Transcribed Image Text:Suppose that {a} and {b} are two sequences of real numbers, and that a → L and n=1 n=1 b → L where L & R and L = ± co Let {} be the 'interlaced' sequence a, b, a, ¹... defined by C2m-1 = am² C2m = bm n=1 Use the definition of limit to show lim c = L. 11 → 00 Definition of limit If X ≤ R, a is a limit point of X, and f: X → R, say that the limit of f on X at a is the number L provided that for every e > 0 there is a 8 > 0 such that f(x) L < € whenever xe X and 0 < |ax| < 8.
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