(2) Let an be the sequence defined by: a₁ = 1 a2 = 2 an an-1 + 2an-2 for n ≥ 3. (a) Find a3,.. (b) Use induction to prove that an > 0 for all n € N. an (c) Use induction to prove that an+1 (d) Use (b) and (c) to conclude that an < an+1 for all n € N. .... ag. < 1 for all n € N.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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(2) Let an be the sequence defined by:
a₁ = 1
a2 = 2
an an-1 + 2an-2 for n ≥ 3.
(a) Find a3,..
(b) Use induction to prove that an > 0 for all n € N.
an
(c) Use induction to prove that
an+1
(d) Use (b) and (c) to conclude that an < an+1 for all n € N.
.... ag.
< 1 for all n € N.
Transcribed Image Text:(2) Let an be the sequence defined by: a₁ = 1 a2 = 2 an an-1 + 2an-2 for n ≥ 3. (a) Find a3,.. (b) Use induction to prove that an > 0 for all n € N. an (c) Use induction to prove that an+1 (d) Use (b) and (c) to conclude that an < an+1 for all n € N. .... ag. < 1 for all n € N.
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