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4. Find the largest number of points which a foot ball team cannot get exactly using just 3-point field goals and 7-point touchdowns. Prove your answer is correct by mathematical induction.

4. Find the largest number of points which a foot ball team cannot get exactly using just 3-point field goals and 7-point touchdowns. Prove your answer is correct by mathematical induction.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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) 4. Find the largest number of points which a foot ball team cannot get exactly using just 3-point field goals and 7-point touchdowns. Prove your answer is correct by mathematical induction. s) 5. Prove, by mathematical induction, that Fo+F+F,+-+F, = F+2-1, where F, is the nth Fibonacci number (Fo = 0, F = 1 and F = F1+F-2). ts) 6. Prove that the sum of the interior angles of a convex n-gon is (n-2) 180°. (A convex n-gon is a polygon with n sides for which each interior angle is less than 180°.) Hint: start with (k+1)-gon and divide it up into a k-gon and a triangle.
Transcribed Image Text:) 4. Find the largest number of points which a foot ball team cannot get exactly using just 3-point field goals and 7-point touchdowns. Prove your answer is correct by mathematical induction. s) 5. Prove, by mathematical induction, that Fo+F+F,+-+F, = F+2-1, where F, is the nth Fibonacci number (Fo = 0, F = 1 and F = F1+F-2). ts) 6. Prove that the sum of the interior angles of a convex n-gon is (n-2) 180°. (A convex n-gon is a polygon with n sides for which each interior angle is less than 180°.) Hint: start with (k+1)-gon and divide it up into a k-gon and a triangle.
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