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

Use mathematical induction to prove that 2² x 5+5² x 8+8² × 11 for n=1,2,.... +...+(3n-1)²(3n+2) = = n(3n-1)(3n+2) (3n + 5)

Use mathematical induction to prove that the following statement is true: 3 × 5 + 7 × 9 + · · · + (4n − 1)(4n + 1) = n(4n+1)(4n+5)/3 for all n ≥ 1.

Consider the following statement. There is an integer n such that 2n² - 5n+ 2 is prime. To prove the statement it suffices to find a value of n such that (n, 2n² – 5n + 2) satisfies the property "2n² – 5n + 2 is prime." Show that you can do this by entering appropriate values for n and 2n² – 5n + 2. (n, 2n² - 5n + 2) =

Use the principle of mathematical induction to establish the given formula. n(n+ 1)(2n + 7) + 2) 9.

I need this question completed in 5 minutes with handwritten working

Use induction to prove that the sum of {n=-2} and {N} (4n − 5) = (n + 3)(2n − 9).

Show that if n is an integer and 5n + 6 is odd, then n is odd. (Use contradiction.)

Prove or disprove

Use mathematical induction to show that n r=1 (2r − 1)² = 1² + 3² +5² + + (2n − 1)² = n(2n − 1)(2n + 1) 3