Given a positive integer n, let a2,n–1 a2,n a3,n-2 a3,n-1 a3,n An = аn-1,2 аn-1,n-2 аn-1,п-1 @n-1,п ... an,1 An,2 An,n-2 An,n-1 An,n whose a¡j entries with i+j< n are all equal to 0. Conjecture a formula for det(An) and prove

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Q: It is given that (²1) = 4, (3) k 2 -(" + ²) Write and expression for = B, (x+1)= = C (where n, k, A,…

A: Use the properties of combination.

Q: 5. (a) Prove the following proposition: For all integers a, b, and d with d 0, if d divides a or d…

A: To Prove :-  For all integers a , b ,d with d≠ 0, if d divides a or d divides b, then d divides the…

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A: Given operation is a*b = 3a+b

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A: Number System

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Q: A is the set of odd number greater than 5 and less than 23 n (A)=

A: A is the set of odd numbers greater than 5 and less than  23

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A: Consider the given information:

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Q: Prove that 2n + 3n is a multiple of 5 for all odd n € N.

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Q: How many integer solutions to x1 + x2 + x3 + x4 x₁ ≥ 4, x2 ≥ 2, x3 ≥ 5 and x4 ≥ 3? > = 31 are there…

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Q: Prove that 6">5" + 9 for any integer n ≥ 2.

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Q: 7. For n ≥ 1, verify that 12+32 +52 ++ (2n- +3²+5² · + 2n-1)² = (2n+1) 3

A: Ans : page 1:Ans page 2:

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A: Given: The statement 1+2+22+⋯+2n=2n+1-1 Proof: Base step: Show the statement is true when n=0.…

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