Using induction, verify that 12 + 32 + 52 + ... + (2n -1)2 = n(2n -1)(2n +1) / 3 is true for every positive integer n.

Q: mathematical induction

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Q: Use mathematical induction to prove that (n³ + 3n² + 2n) is divisible by 3 for all n > 1.

A: See the attachment

Q: O Prove 1+3+ 9+27+ ·+ 3n-1 = 3"-1 for any positive integer n. %3D

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Q: Use mathematical induction to prove that the statement, 3 is a factor of n(n+1)(n - 1) is true for…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Take any arbitrary integer n and then square it, which one is true? n2 cannot be in the form 7k + 5.…

A: Solution is given as follows :

Q: Can you use mathematical induction to show that 4 divides 32x + 7 First define the predicate ?(x)

A: given , expression :- 32x+7 we have to prove that given expression is divisible by 4 .

Q: 3. Using induction, verify that 12 + 3 + 5² + (2n – 1)² = n(2n–1)(2n+1) is true for every positive…

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Q: Use the method of mathematical induction to show that n³ +5n is divisible by 3 for all positive…

A: Induction is show below

Q: Prove by the method of Mathematical Induction that, 3 divides n3 + 2n for any positive integer n.

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Q: Use induction to prove that the product of any three consecutive positive integers is divisible by…

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Q: Find each (n+3)(n+2) (4n 5)(3n + 2) (n+7)(n + 5)

A: Since you have posted multiple subparts we solve the first three subparts for you to get the…

Q: Use mathematical induction to prove 1+ 2+ 22 · · ·+ 2n = 2n+1−1 for each integer n ≥ 0

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Q: With induction, prove that 1*2 to the power of 0 + 2*2 to the power of 1 + 3* 2 to the power of 2 +…

A: To prove

Q: Use mathematical induction to prove that 1 + 2 + ⋯ + ? =n(n + 1)/2 for each positive integer ?.

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Q: Prove that a number in the form 6k+5,” what I mean is a number in the form of 6 times some integer…

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Q: 21 divides 4(n+1) + 5(2n-1) whenever n is a positive integer.

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Use induction to show that n4 + 15 is a multiple of 16 for every positive odd integer n.

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Q: Prove that for a positive integer n we have that 33n+3 – 26n – 27 is divisible by 169. - -

A: The given expression is: 33n+3-26n-27 This is to be proved that the expression is divisible by 169.

Q: Add the polynomials (10z - 82 7æ³ - 10) + (- 4x + 12a + 7a + 9) | Submit Question

A: Add the polynomials. Solution is given below-

Q: Use induction to prove that 3 | (10n+1 + 10n + 1) for all positive integers n

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Q: let a=2+7i b=4-2i Choose the correct result of a/b*

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Q: how that 1+2+2²+23+...+2 = 2n+1 -1 for n≥ 0.

A: We need to prove by induction hypothesis      1+2+22+.........+2n=2n+1-1, for n≥0

Q: divisible by 3 for

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Q: Q5. Describe the principle of mathematical induction and prove P(n) =1 + 2 + 22 +..+ 2" = 2n+1 - 1…

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Q: 2 is a factor of n2 + 3n.Use mathematical induction to prove that the statement is true for every…

A: To prove : n2+3n is divisible by 2 or 2 is a factor of n2+3n for every positive integer n. Proof :…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Prove by induction that 1² +2² +3²+...+ n² n(n + 1)(2n + 1) 6

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Q: Use induction to prove that 3 | (2²n — 1) for all nonnegative integers n.

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Q: Derive an expression for the sum of the first n positive even integers.

A: We Use the A.P series. Find The sum of the first n positive even integer.

Q: Show that (a) 8n −3n is divisible by 5 for all natural numbers n.  (b) n2 −n +41 is odd for all…

A: expansion of (a+b)n = hco an bo + nc1 an-1 b1 +.......... +ncn ao b n

Q: this

A: We use definition of t(n).

Q: Find the product 3/2 (5 /12 + 6/6) and express your answer in the form A/B+ CVD, A, B, C, and D are…

A: Given : 32512 + 66

Q: Can you assist  me in  verifing    that    for    all    n ≥ 1,    the    sum    of    the    first…

A: Here, we have to verify that ∀n≥1, the sum of the squares of the first 2n positive integers is given…

Q: Show that x2 + 9 is prime.

A: To show x2 + 9 is prime.