Consider the following sequence defined recursively: a1 %3D 5, аz 3D 8, аm+1 —D 2а, — ап-: 2an - an-

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Consider the following sequence defined recursively:
aj = 5, a2 = 8, an+1 = 2an – an-1 + 2, n > 2.
Prove that an = n² + 4 for all n E N.
Transcribed Image Text:Consider the following sequence defined recursively: aj = 5, a2 = 8, an+1 = 2an – an-1 + 2, n > 2. Prove that an = n² + 4 for all n E N.
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