Question

Main topic and problems for the final project The main purpose of the project is to introduce you how to use a in an computer as a research tool Introductory Discrete Mathematics. In this project you will be asked to show how the Fibonacci sequence {Fn} is related to Pascal's triangle using the following identities by hand for small and then by computers with large n. Finally, to rove the identity by mathematical arguments, such as inductions or combinatorics. I just need I k Fe answers for 3, 4 k-0 where F is the t-th term of the Fibonacci sequence. and 5 equal to the corresponding Hint: In that the sum of the diagonals of Pascal's triangle are Fibonacci sequence term. That is the values on the diagonals of Pascal's triangle add up to the Fibonacci numbers. Problems: (1) By hand, show that the above identity is true for some smallne {1,2,...,7} (2) By computer, show that the above identity is true for some large n e {1,2,..., 100). (a) Write a program with any language for the left-hand side of the identity. (b) Write a program with any language to print out for the right-hand side of the identity. (c) Compare the result from part (a) and (b) for some (3) Prove the identity by mathematical induction by hand. (4) Prove the identity by combinatorial arguments. large n E {1,2,... , 100} Problemonumberon Prove the identity by mathematical induction with computers. REFERENCES Discrete Mathematics and Its Applications, Author: Kenneth H. Rosen, Publisher: McGraw- Hill, Edition: 7, Year Published: 2012.

Answer 1

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