# Mathematical Induction

## Prove that n^3-n is divisible by 3

Given n3 – n is divisible by 3 ∀ n ∈ N Proof We will prove the given statement by induction STEP 1 n = 1 n3 – n = 13 – 1 = 0 0 is divisible by 3. Therefore, the statement is true for n = 1 STEP 2 Let the given statement …

## Prove by induction n^3+(n+1)^3+(n+2)^3 is divisible by 9

Given n3 + (n + 1)3 + (n + 2)3 is divisible by 9 ∀ n ∈ N Proof We will prove the given statement by induction STEP 1 n = 1 13 + (1 + 1)3 + (1 + 2)3= 13 + 23 + 33 = 1 + 8 + 27 = 36 36 …

## Prove by induction that 6^n-1 is divisible by 5

Given 6n – 1 is divisible by 5 ∀ n ∈ N Proof We will prove the given statement by induction STEP 1 n = 1 6n – 1 = 61 – 1 = 5 5 is divisible by 5. Therefore, the statement is true for n = 1 STEP 2 Let the given statement …

## Prove 4^n-1 is divisible by 3

Given 4n – 1 is divisible by 3 ∀ n ∈ N Proof We will prove the given statement by induction STEP 1 n = 1 4n – 1 = 41 – 1 = 3 3 is divisible by 3. Therefore, the statement is true for n = 1 STEP 2 Let the given statement …

## Prove that n^3-n is divisible by 6

Given n3 – n is divisible by 6 ∀ n ∈ N Proof We will prove the given statement by induction STEP 1 n = 1 n3 – n = 13 – 1 = 0 0 is divisible by 6. Therefore, the statement is true for n = 1 STEP 2 Let the given statement …