Question

Consider the following expression: 7^n-6*n-1 Using induction, prove the expression is divisible by 36. I understand...

Consider the following expression: 7^n-6*n-1

Using induction, prove the expression is divisible by 36.

I understand the process of mathematical induction, however I do not understand how the solution showed the result for P_n+1 is divisible by 36? How can we be sure something is divisible by 36? Please explain in great detail.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
prove by induction that n(n+1)(n+2) is divisible by 6 for n=1,2...
prove by induction that n(n+1)(n+2) is divisible by 6 for n=1,2...
Using induction, prove the following: i.) If a > -1 and n is a natural number,...
Using induction, prove the following: i.) If a > -1 and n is a natural number, then (1 + a)^n >= 1 + na ii.) If a and b are natural numbers, then a + b and ab are also natural
1. Prove that an integer a is divisible by 5 if and only if a2 is...
1. Prove that an integer a is divisible by 5 if and only if a2 is divisible by 5. 2. Deduce that 98765432 is not a perfect square. Hint: You can use any theorem/proposition or whatever was proved in class. 3. Prove that for all integers n,a,b and c, if n | (a−b) and n | (b−c) then n | (a−c). 4. Prove that for any two consecutive integers, n and n + 1 we have that gcd(n,n + 1)...
Without using induction, prove that for x is an odd, positive integer, 3x ≡−1 (mod 4)....
Without using induction, prove that for x is an odd, positive integer, 3x ≡−1 (mod 4). I'm not sure how to approach the problem. I thought to assume that x=2a+1 and then show that 3^x +1 is divisible by 4 and thus congruent to 3x=-1(mod4) but I'm stuck.
Prove the following statement by mathematical induction. For every integer n ≥ 0, 2n <(n +...
Prove the following statement by mathematical induction. For every integer n ≥ 0, 2n <(n + 2)! Proof (by mathematical induction): Let P(n) be the inequality 2n < (n + 2)!. We will show that P(n) is true for every integer n ≥ 0. Show that P(0) is true: Before simplifying, the left-hand side of P(0) is _______ and the right-hand side is ______ . The fact that the statement is true can be deduced from that fact that 20...
Prove by mathematical induction that for all odd n ∈ N we have 8|(n2 − 1)....
Prove by mathematical induction that for all odd n ∈ N we have 8|(n2 − 1). To receive credit for this problem, you must show all of your work with correct notation and language, write complete sentences, explain your reasoning, and do not leave out any details. Further hints: write n=2s+1 and write your problem statement in terms of P(s).
1) Find the sum S of the series where S = Σ i ai -- here...
1) Find the sum S of the series where S = Σ i ai -- here i varies from 1 to n. Use the mathematical induction to prove the following: 2) 13 + 33 + 53 + …. + (2n-1)3 = n2(2n2-1) 3) Show that n! > 2n for all n > 3. 4) Show that 9(9n -1) – 8n is divisible by 64. Show all the steps and calculations for each of the above and explain your answer in...
Problem 3. Let n ∈ N. Prove, using induction, that Σi^2= Σ(n + 1 − i)(2i...
Problem 3. Let n ∈ N. Prove, using induction, that Σi^2= Σ(n + 1 − i)(2i − 1). Note: Start by expanding the righthand side, then look at the following pyramid (see link) from
Prove the following using induction: (a) For all natural numbers n>2, 2n>2n+1 (b) For all positive...
Prove the following using induction: (a) For all natural numbers n>2, 2n>2n+1 (b) For all positive integersn, 1^3+3^3+5^3+···+(2^n−1)^3=n^2(2n^2−1) (c) For all positive natural numbers n,5/4·8^n+3^(3n−1) is divisible by 19
Prove the following result. PLEASE EXPLAIN reasoning so I can understand how to do it on...
Prove the following result. PLEASE EXPLAIN reasoning so I can understand how to do it on my own. Let x and y be integers. Then x ≡ y (mod m) and x ≡ y (mod n) if and only if x ≡ y (mod L), where L = lcm[m, n]. Then expand to any finite number of moduli
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT