1. a² - a = a (a - 1) = (a - 1) x a
since a-1 and a are two consecutive whole number, one of them is "even" whole number. Therefore (a² - a) is divisible by 2 for any whole value of a.
2. 2ⁿ + 2ⁿ⁺¹ + 2ⁿ⁺² = 2ⁿ⁻¹ x (2 + 2² + 2³) = 2ⁿ⁻¹ x 14
So, the sum of three consecutive exponents of the number 2 is divisible by 14.
So you want to prove . Notice that for , we have
If , we have
and we know , so will always be a multiple of 14 and we're done.
what i would say the best answer is a. 40.5