Prove that n^3-7n+3 is divisible by 3
Given n3 – 7n + 3 is divisible by 3 ∀ n ∈ N Proof We will prove the given statement by induction STEP 1 n = 1 n3 – 7n + 3 = 13 – 7*1 + 3 = -3 -3 is divisible by 3. Therefore, the statement is true for n = 1 …
Given n3 – 7n + 3 is divisible by 3 ∀ n ∈ N Proof We will prove the given statement by induction STEP 1 n = 1 n3 – 7n + 3 = 13 – 7*1 + 3 = -3 -3 is divisible by 3. Therefore, the statement is true for n = 1 …
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 …
Given n3+ 2 is not divisible by 8 ∀ n ∈ N Proof For value of n, we have 2 cases CASE 1 : n is odd If n is odd then n3 is also odd. We know ODD + EVEN = ODD. Therefore, n3+2 is odd. 8 cannot divide an odd number. We can …
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 n^3+(n+1)^3+(n+2)^3 is divisible by 9 Read More »
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 …
Given n2 – 2 is not divisible by 4 ∀ n ∈ N Proof For value of n, we have 2 choice CASE 1 : n is even If n is even, then we can write n as n = 2x, x ∈ N n2 – 2 = 4×2 – 2 = 2( 2×2 – …
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 …
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 …
For the value of n, we have 3 choices Case 1 : n % 3 = 1 Let, P = (n2+2) % 3 P = ( ( n2 ) % 3 + 2 % 3 ) % 3 P = ( ( n % 3 ) ( n % 3 ) + 2 ) % …
Prove that if n is not divisible by 3 then n^2+2 is divisible by 3 Read More »
Given if n is odd then 8 divides n2-1 Proof We can proof the given statement directly. Let n ∈ O Let, P = n2 – 1 We need to prove that P is divisible by 8 P = n2 – 12 P = (n + 1)(n – 1) We know that n is odd. …