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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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