In exercises 8 through 14, prove the given statement using induction. 1 1 + 4.7 (3n - 2)(3n+1) 8. + = n 3n+ 1

Q: Use mathematical induction to prove that the statement is true for every positive integer n.

A: To prove the statement 1 + 4 + 42 + ... + 4n - 1 = 4n - 13 is true for every positive integer n…

Q: Show by induction that 1+3 +5+ . + (2n – 1) = n² ...

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Q: se mathematical induction to prove that the following statement is true: n(4n+ 1)(4n+5) 3x5+7x9++…

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Q: Prove that n3 + 2n is divisible by 3 for all n E N.

A: We prove that n3+2n is divisible by 3 for all natural numbers n.

Q: Induction: m (2n-1); nz n=? • Prove by Mathematical 1+5+9+...+(4n-3)

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Q: 1² +2²+3² 2 +...+ n² = n(n+1)(2n+1) 6

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Q: 4 + 8 + 12 + . . . + 4n = 2n(n + 1).Use mathematical induction to prove that the statement is true…

A: To prove: 4+8+12+...+4n=2nn+1. It is proved by mathematical induction. For n=1 4=211+1=4 Here, the…

Q: Prove the statement by induction .+ (4n – 2) = 2n² 2. 1+ 4 + 7 + . + (3n-2) = n ( 3n - 1) 1. 2 + 6 +…

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Q: prove the statement is true by using Mathematical Induction.  1 + 2n < 3n for all n ≥ 2

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Q: 5) Use induction to prove that 4" -1 is divisible by 3 for all integer n21.

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Q: . Use mathematical induction to show that n Σ r=1 (2r − 1)² = 1² + 3² +5² + + (2n − 1)² = = n(2n −…

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Q: "ou MUST answer question # 1. Then, choose Ol Use mathematical induction to prove the form…

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Q: Show that 1+5+9+...+ (4n-3) = 2n²n using mathematical. induction.

A: Base case:    For n = 1:          LHS = 1          RHS = 2.12 - 1 = 2 - 1 = 1      So, LHS = RHS.…

Q: 19. Prove 1+ 10 + 102 + 103 + 10* + .+ 10k-1 = (10k – 1) using the principle of ... mathematical…

A: we have to prove by mathematical induction

Q: 1+4+7+10++ (3n-2)=2(3n - 1)

A: Consider the statement

Q: Use the mathematical induction to prove that an = 4n+1 + 52n-1 is divisible by 21 for any nЄ N.

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Q: Using induction, prove that 5|62n) – 1 for n = 1, 2, 3, ... %3D

A: Principle of Mathematical Induction: Mathematical Induction is a technique of proving a statement,…

Q: 4. For n > 1, use mathematical induction to establish each of the following divisibility statements:…

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Q: Which of the following is true and which is not? sh mathematical induction ? 1)3" + 1 is divisible…

A: In this question we will use basic of calculus i.e concept of divisibility of a number. Solution of…