The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13,... (where Fo = 0). (a) Write out the first few terms of the sequence of partial sums: 0, 0 + 1, 0+1+1,... (b) Guess a formula for the sequence of partial sums expressed in terms of a single Fibonacci number. For example, you might say Fo + F₁ + + Fn = 3F² + n, although that is definitely not n-1 correct.

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Chapter2: Second-order Linear Odes
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Please try to explain the answer for 5(b) (dont use sigma to solve this problem)

5. The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, ... (where Fo = 0).
(a) Write out the first few terms of the sequence of partial sums: 0,
0 + 1, 0+1+1,. . .
(b) Guess a formula for the sequence of partial sums expressed in
terms of a single Fibonacci number. For example, you might
say Fo + F₁ + ... + Fn = 3F²_₁ + n, although that is definitely not
n-1
correct.
Transcribed Image Text:5. The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, ... (where Fo = 0). (a) Write out the first few terms of the sequence of partial sums: 0, 0 + 1, 0+1+1,. . . (b) Guess a formula for the sequence of partial sums expressed in terms of a single Fibonacci number. For example, you might say Fo + F₁ + ... + Fn = 3F²_₁ + n, although that is definitely not n-1 correct.
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