3. Answer any one of 3(a) and 3(b). (a) Use mathematical induction to prove the following inequality: 4n > 1+ 3n for all positive integers n. (b) Prove that E, i (2²-1) = (n – 1)2" + 1 for all positive integers n using mathematical induction.

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Q: 3. Use the Principle of Mathematical Induction to prove that for a natural number n, n(n + 1)(2n +…

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Q: 1+ x Σ Aa" (1 – 2)? n=0

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Q: 2. Using the mathematical induction, prove Σ (k² + 2k-2) = n(2n² + 9n - 5), k=1

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A: For   So it is true.

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Q: For positive integers n and k (k sn+ 1), the kth term of (a + b)n is given by

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Q: (1) Prove by induction: Σ₁(i² − i + 1) = n³+2n

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Q: Prove by induction that for positive integers n, 13 | (4²n+1 + 3n−1).

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Q: (1) Prove by induction: Σ²₁ (i² − i + 1) = n³+2n

A: (1)  Let the given statement is  P n :  ∑i=1n i2 - i + 1 = n3 + 2n3             For  n = 1  we get…

Q: For each integer n2 2, let P(n) be the following equation (n – 1)n(2n + 5) (i – 1)(i + 1) = 72 - 6…

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Q: (Vn)(n2 +n+ 17 is prime)

A: Since, you have posted multiple questions , I am doing the very question (ques 7)  according to our…

Q: (2) Give a proof by induction of the formula: P(n): 12 +22 + ...+ n² = "(n+ 1)(2n + 1) 6

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Q: Select all of the following that are equivalent to >(2) +> (3k + 1)? k=0 k=0 п+1 A. O) (3k + 3) k=0…

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Q: prove using induction: II ( 1 1 1 П 2k +1 2k+2, for n 20 (2n + 2)! k-0

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A: Mathemetical Induction

Q: Directions: Prove using induction. 3(5"+1 -1) 1. 3+3 5+3-52 +...+3 5" = for n a nonnegative integer.…

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