(1) A sequence an is given by a₁ = √2, an+1 √2+ an (a) By induction or otherwise, show that a,, is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that exists. (b) Find limn-+0 an.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.3: Geometric Sequences
Problem 52SE: Use explicit formulas to give two examples of geometric sequences whose 7thterms are 1024.
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(1) A sequence an is given by a₁ =
√2, an+1 = √2+ an.
(a) By induction or otherwise, show that an is increasing and
bounded above by 3. Apply the Monotonic Sequence Theorem
to show that exists.
(b) Find limn-+0 an.
Transcribed Image Text:(1) A sequence an is given by a₁ = √2, an+1 = √2+ an. (a) By induction or otherwise, show that an is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that exists. (b) Find limn-+0 an.
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