Show that for any integer n ≥ 2, C(2n,n) > C(2n,n-1)

Q: For all n ≥ 1, let an = (a) Find a1, a2, A3, A4. (b) Computea. i=1 (c) Computea. i=1 (n + 1)² n!…

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Q: determine the value of c(n,5) /p(n,5) where n can be any integer thats 5 or greater

A: Recall the following. Permutations Number of permutations of n things taken r at a time: pn,r=n!n-r!…

Q: Find a given that ||a i+ (a – 1)j + (a + 1)k|| = 7.

A: Given:

Q: Show that (n) ‡ 14 for all n ≥ 1.

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Q: Prove the claim that there are no integers j and k such that j^2 + 3k^2 = 8

A: Since both j and k are being squared so if we prove the case for positive integers, that will prove…

Q: For integers n>r> 0, use the definition of the factorial function to prove that (n − 1)! (n − 1)! n!…

A: By the definition of factorial function, the factorial of a non-negative integer n, denoted by n!,…

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

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