Looking for some help in proving this sequence is Cauchy.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 46E
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Looking for some help in proving this sequence is Cauchy.
2n + 1
1. Use the definition to prove that the sequence
is Cauchy
nEN
2. Let x E (0, 1), use e – d to prove
V4+x – 2
lim
1
4
3. Let a, b, c, d E R. Define explicitly a bijection from [a, b] onto [c, d].
an
4. Let a1 = 1,
An+1 =
for n > 1. Show that lim an exists and find the limit.
V 2
5. Prove or disprove that if {a,} and {b,} are Cauchy and b, # 0. Then
San l
is Cauchy
Transcribed Image Text:2n + 1 1. Use the definition to prove that the sequence is Cauchy nEN 2. Let x E (0, 1), use e – d to prove V4+x – 2 lim 1 4 3. Let a, b, c, d E R. Define explicitly a bijection from [a, b] onto [c, d]. an 4. Let a1 = 1, An+1 = for n > 1. Show that lim an exists and find the limit. V 2 5. Prove or disprove that if {a,} and {b,} are Cauchy and b, # 0. Then San l is Cauchy
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