(a) Let {n} be a sequence such that there exist A> 0 and c € (0, 1) for which n+1- n ≤ Ac" for all nEN. Is In a Cauchy sequence? Is this conclusion still valid if we assume n+1-In = 0? lim 81x

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(a) Let {rn} be a sequence such that there exist A>0 and c e (0, 1) for which |rn+1 – Xn] < Ac" for all
ne N. Is r, a Cauchy sequence ? Is this conclusion still valid if we assume
lim |rn+1 – xn| = 0?
Transcribed Image Text:(a) Let {rn} be a sequence such that there exist A>0 and c e (0, 1) for which |rn+1 – Xn] < Ac" for all ne N. Is r, a Cauchy sequence ? Is this conclusion still valid if we assume lim |rn+1 – xn| = 0?
(b) With the help of Sandwich theorem (or Squeeze theorem), show that
lim (2 V – 1)" = x² for r > 1.
%3D
Transcribed Image Text:(b) With the help of Sandwich theorem (or Squeeze theorem), show that lim (2 V – 1)" = x² for r > 1. %3D
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