Use mathematical induction to show n ≥ 0, 8n -2n is divisible by 6

Using induction, verify that 2^2+4^2+...+(2n)^2 = 2n(n+1)(2n+1) / 3 is true for every positive integer n.  Discrete Math.

Use mathematical induction to prove each of the following: * (a) For each natural number n, 3 divides (4" - 1). (b) For each natural number n, 6 divides (n³ − n).

Use Induction proof

For every integer n23 I+ 2+ 22+ + 니^ 4(40-l6) %3D 3. Proof (by induction)

Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 9+19+29++ (10n-1) = n(5n+ 4) 2 To prove that 9+19+29++ (10n-1) = n(5n+ 4) is true for all natural numbers n, first show that this statement is true for n= Simplify each side of the statement for the appropriate value of n. 9+19+29++ (10n-1) = n(5n+4) What is the next step in this induction proof? O A. Determine whether the statement holds for any number k + 1. OB. Assume the statement holds for some k, and determine whether it then holds for k + 1. OC. Determine whether the statement holds for some k. If so, it also holds for k + 1.

Use mathematical induction to prove the statement n^3+3n is divisible by 2 for all n > =1

Show that n! > 3ª for n > 7.

Establish the formula by mathematical induction

Show that if 2n−1 is prime then n is prime.