Prove the following statement by mathematical induction.For every integer n ≥ 0, 7n − 1 is divisible by 6.Proof (by mathematical induction): Let P(n) be the following sentence.7n − 1 is divisible by 6.We will show that P(n) is true for every integer n ≥ 0.Show that P(0) is true: Select P(0) from the choices below.6 | (70 − 1)(70 − 1) | 6    6 is a multiple of 70 − 11 is a factor of 70 − 1The truth of the selected statement follows from the definition of divisibility and the fact that 70 − 1 =

Prove the following statement by mathematical induction.For every integer n ≥ 0, 7n − 2n is divisible by 5.Proof (by mathematical induction): Let P(n) be the following sentence.7n − 2n is divisible by 5.We will show that P(n) is true for every integer n ≥ 0.Show that P(0) is true: Select P(0) from the choices below.5 | (70 − 20)70 − 20 < 5    (70 − 20) | 55 is a multiple of 70 − 20The truth of the selected statement follows from the definition of divisibility and the fact that 70 − = 0.Show that for each integer k ≥ 0, if P(k) is true, then P(k + 1) is true: Let k be any integer with k ≥ 0, and suppose that P(k) is true. Select P(k) from the choices below.5 is a multiple of 7k − 2k5 is divisible by 7k − 2k    7k − 2k is divisible by 57k − 2k < 5[This is P(k), the inductive hypothesis.]We must show that P(k + 1) is true. Select P(k + 1) from the choices below.5 is a multiple of 7k + 1 − 2k + 17k + 1 − 2k + 1 < 5    7k + 1 − 2k + 1 is divisible by 55 is divisible by 7k + 1 − 2k + 1

Problem 3. Prove that 7n − 6n − 1 is divisible by 36 for all n ∈ N.

Which statement is true about the divisibility rule of 6?Group of answer choicesA number is divisible by 6 if the sum of all its digits is divisible by 6.A number is divisible by 6 if it is divisible by 2 or 3.A number is divisible by 6 if it is divisible by both 2 and 3.A number is divisible by 6 if it ends in even number. PreviousNext

How many three digit numbers are there divisible by 7

Is 700 953 divisible by 6?yesnoSubmit