07.04 Mathematical InductionAssignment Name: ___________________________________Print this page or copy and paste this assignment in to a word document.After filling in the requested information below, you may either scan your handwritten work or take a clear digital picture. You will need to save the scanned copy or digital picture of your work in order to submit as a file attachment.Note: When saving files, please remember that you should not use a period or a space in your file name. It is recommended that you use the underscore when saving your documents: 1_01, 1_02pg1, 1_02og2, etc. Contact your instructor if you have questions about saving files.Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.(4 points each.)4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = 12 + 42 + 72 + ... + (3n - 2)2 = For the given statement Pn, write the statements P1, Pk, and Pk+1.(2 points)2 + 4 + 6 + . . . + 2n = n(n+1)

OverviewAnalyze motorized traffic flows for a transportation department, using a weighted graph. Then, streamline the design and development process and improve scheduling for several systems engineering projects, using PERT analysis and critical path management.For this assessment, you will demonstrate your ability to use graphs and trees in application modeling, analysis, and optimization.ContextThe