(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.
(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.
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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Question
![(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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38e0ef70-34a2-4c97-b7a1-554a98eb604b%2Ff1faed05-0de7-4fc0-a954-f49460d146c4%2F2frwemp_processed.jpeg&w=3840&q=75)
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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