Question

1. Prove that the value of the expression a^2–a is divisible by 2 for any whole value of a.
2. Prove that the sum of three consecutive exponents of the number 2 is divisible by 14.

Answer 1

Answer:

in steps

Step-by-step explanation:

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.