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Tick all the questions or statements that can be proven or answered using mathematical induction. Between any two positive integers, there are infinitely many rational numbers. Define a recurrence relation by æ1 = 1, æn+1 = /I+2xn for n > 1 Then an <4 for all positive integers n . If n is a positive integer that exceeds 1, then nº + 4" can never be a prime number. n3 + 2n is divisible by 3 for all positive integers n. O There are n identical cars placed randomly around a circular track. If we add up all the fuel in each car, there is exactly enough fuel for a single car to make one complete round. Show that we can always find at least one car amongst the n cars such that it can complete one round by collecting fuel from every car that it passes. E- (k4 + 3k) = 30n(n + 1)(6n³ + 9n² +n + 44) for any positive integer n . ñ is either an integer or is an irrational number for any positive integer n .

Tick all the questions or statements that can be proven or answered using mathematical induction. Between any two positive integers, there are infinitely many rational numbers. Define a recurrence relation by æ1 = 1, æn+1 = /I+2xn for n > 1 Then an <4 for all positive integers n . If n is a positive integer that exceeds 1, then nº + 4" can never be a prime number. n3 + 2n is divisible by 3 for all positive integers n. O There are n identical cars placed randomly around a circular track. If we add up all the fuel in each car, there is exactly enough fuel for a single car to make one complete round. Show that we can always find at least one car amongst the n cars such that it can complete one round by collecting fuel from every car that it passes. E- (k4 + 3k) = 30n(n + 1)(6n³ + 9n² +n + 44) for any positive integer n . ñ is either an integer or is an irrational number for any positive integer n .

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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Tick all the questions or statements that can be proven or answered using mathematical induction. Between any two positive integers, there are infinitely many rational numbers. O Define a recurrence relation by æ1 =1 , æn+1 = /T+ 2xn for n > 1 Then æn < 4 for all positive integers n . O If n is a positive integer that exceeds 1, then n4 + 4" can never be a prime number. n3 + 2n is divisible by 3 for all positive integers n . There are n identical cars placed randomly around a circular track. If we add up all the fuel in each car, there is exactly enough fuel for a single car to make one complete round. Show that we can always find at least one car amongst the n cars such that it can complete one round by collecting fuel from every car that it passes. O D (k4 + 3k) = 30n(n + 1)(6n³ + 9n? + n + 44) for any positive integer n . O vn is either an integer or is an irrational number for any positive integer n.
Transcribed Image Text:Tick all the questions or statements that can be proven or answered using mathematical induction. Between any two positive integers, there are infinitely many rational numbers. O Define a recurrence relation by æ1 =1 , æn+1 = /T+ 2xn for n > 1 Then æn < 4 for all positive integers n . O If n is a positive integer that exceeds 1, then n4 + 4" can never be a prime number. n3 + 2n is divisible by 3 for all positive integers n . There are n identical cars placed randomly around a circular track. If we add up all the fuel in each car, there is exactly enough fuel for a single car to make one complete round. Show that we can always find at least one car amongst the n cars such that it can complete one round by collecting fuel from every car that it passes. O D (k4 + 3k) = 30n(n + 1)(6n³ + 9n? + n + 44) for any positive integer n . O vn is either an integer or is an irrational number for any positive integer n.
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