Problem 7 ii (Explore Fibonacci Partial Sums). Let F. 에 be the Fibonacci sequence. (a) Find the ...
discrete math Problem 7.8 (Explore: Fibonacci Identities). The Fibonacci numbers are a famous integer sequence: Fn) o 0, 1, 1,2,3, 5, 8, 13, 21, 34, 55, 89,... defined recursively by Fo 0, F1, and F F Fn-2 for n2 2. (a) Find the partial sums Fo+Fi +F2, Fo+ Fi +F2Fs, Fo + Fi + F2+Fs +F, FoF1+F2+ Fs+F4F (b) Compare your partial sums above with the terms of the Fibonacci sequence. Do you see any patterns? Make a conjecture for...
Exercise 6. Let En be the sequence of Fibonacci numbers: Fo = 0, F1 = 1, and Fn+2 = Fn+1 + Fn for all natural numbers n. For example, F2 = Fi + Fo=1+0=1 and F3 = F2 + F1 = 1+1 = 2. Prove that Fn = Fla" – BM) for all natural numbers n, where 1 + a=1+ V5 B-1-15 =- 2 Hint: Use strong induction. Notice that a +1 = a and +1 = B2!
I would appreciate any help on this problem for discrete math. Thanks! (: 15. (Q1, P4) Consider the sequence of partial sums of squares of Fibonacci numbers Just to check that we're all on the same page, this sequence starts 1, 2, 6, 15,40, (a) Guess a formula for the nth partial sum, in terms of Fibonacci numbers. (Hint: Write each term as a product.) (b) Prove your formula is correct by mathematical induction. (c) Explain what this problem has...