Question

prove that for every integer m, the number (m^3 +3m^2 +2m)/6 is also an integer can...

prove that for every integer m, the number (m^3 +3m^2 +2m)/6 is also an integer

can I get a step by step induction proof please.

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
Statement 3. If m is an even integer, then 3m + 5 is an odd integer....
Statement 3. If m is an even integer, then 3m + 5 is an odd integer. a. Play with the statement - i.e., Look at/test a few examples. (See if there are any counter-examples.) b. Write a proof of this statement. (Hint: 5 = 4 + 1 = 2(2) + 1) Remark 1. Let's recap some important properties about odd and even that we have seen (in notes and this activity): i. If a and b are even, then ab...
“For every nonnegative integer n, (8n – 3n) is a multiple of 5.” (That is, “For...
“For every nonnegative integer n, (8n – 3n) is a multiple of 5.” (That is, “For every n≥0, (8n – 3n) = 5m, for some m∈Z.” ) State what must be proved in the basis step.     Prove the basis step.     State the conditional expression that must be proven in the inductive step.   State what is assumed true in the inductive hypothesis. For this problem, you do not have to complete the inductive step proof. However, assuming the inductive step proof...
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...
Use strong induction to prove that every natural number n ≥ 2 can be written as...
Use strong induction to prove that every natural number n ≥ 2 can be written as n = 2x + 3y, where x and y are integers greater than or equal to 0. Show the induction step and hypothesis along with any cases
Prove the following theorem: For every integer n, there is an even integer k such that...
Prove the following theorem: For every integer n, there is an even integer k such that n ≤ k+1 < n + 2. Your proof must be succinct and cannot contain more than 60 words, with equations or inequalities counting as one word. Type your proof into the answer box. If you need to use the less than or equal symbol, you can type it as <= or ≤, but the proof can be completed without it.
Prove the following theorem: For every integer n, there is an even integer k such that...
Prove the following theorem: For every integer n, there is an even integer k such that n ≤ k+1 < n + 2. Your proof must be succinct and cannot contain more than 60 words, with equations or inequalities counting as one word. Type your proof into the answer box. If you need to use the less than or equal symbol, you can type it as <= or ≤, but the proof can be completed without it.
5. Use strong induction to prove that for every integer n ≥ 6, we have n...
5. Use strong induction to prove that for every integer n ≥ 6, we have n = 3a + 4b for some nonnegative integers a and b.
Prove that for every natural number m, it holds 2*m + 1 ≤ 3^m. .
Prove that for every natural number m, it holds 2*m + 1 ≤ 3^m. .
3.a) Let n be an integer. Prove that if n is odd, then (n^2) is also...
3.a) Let n be an integer. Prove that if n is odd, then (n^2) is also odd. 3.b) Let x and y be integers. Prove that if x is even and y is divisible by 3, then the product xy is divisible by 6. 3.c) Let a and b be real numbers. Prove that if 0 < b < a, then (a^2) − ab > 0.
Discrete Math 6. Prove that for all positive integer n, there exists an even positive integer...
Discrete Math 6. Prove that for all positive integer n, there exists an even positive integer k such that n < k + 3 ≤ n + 2 . (You can use that facts without proof that even plus even is even or/and even plus odd is odd.)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT