Question

Prove n+1 < n for n>0 Assume for a value k; K+1< K We now do...

Prove n+1 < n for n>0 Assume for a value k; K+1< K We now do the inductive hypothesis, by adding 1 to each side K+1+1 < k+1 => K+2< k+1 Thus we show that for all consecutive integers k; k+1> k Where did we go wrong?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
How do I prove "there are no integers k > 1 and n > 0 such...
How do I prove "there are no integers k > 1 and n > 0 such that k^2 +1 = 2^n.
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 that lim n^k*x^n=0 as n approaches +infinity. Where -1<x<1 and k is in N.
Prove that lim n^k*x^n=0 as n approaches +infinity. Where -1<x<1 and k is in N.
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)...
Prove that there exist n consecutive positive integers each having a (nontrivial) square factor. How would...
Prove that there exist n consecutive positive integers each having a (nontrivial) square factor. How would you then modify your proof so that each of these integers instead has a cube factor (or more generally, a kth power factor where k ≥ 2)? This is a number theory question. Please show all steps and make clear notes about what is happening for a clear understanding. Please write clearly or do in latex. Thank you
Problem 1. Prove that for all positive integers n, we have 1 + 3 + ....
Problem 1. Prove that for all positive integers n, we have 1 + 3 + . . . + (2n − 1) = n ^2 .
Let A ={1-1/n | n is a natural number} Prove that 0 is a lower bound...
Let A ={1-1/n | n is a natural number} Prove that 0 is a lower bound and 1 is an upper bound:  Start by taking x in A.  Then x = 1-1/n for some natural number n.  Starting from the fact that 0 < 1/n < 1 do some algebra and arithmetic to get to 0 < 1-1/n <1. Prove that lub(A) = 1:  Suppose that r is another upper bound.  Then wts that r<= 1.  Suppose not.  Then r<1.  So 1-r>0....
Prove that, for every k > 1, there is a n such that each of n+1,...
Prove that, for every k > 1, there is a n such that each of n+1, n+2, ···, n + k is not a prime number.
We denote {0, 1}n by sequences of 0’s and 1’s of length n. Show that it...
We denote {0, 1}n by sequences of 0’s and 1’s of length n. Show that it is possible to order elements of {0, 1}n so that two consecutive strings are different only in one position
Given A is a mxn matrix with dim(N(A)) if u=(α(1), α(2),..., α(n))^T ∈N(A). Prove that α(1)a(1)+α(2)a(2)+...+α(n)a(n)=0,...
Given A is a mxn matrix with dim(N(A)) if u=(α(1), α(2),..., α(n))^T ∈N(A). Prove that α(1)a(1)+α(2)a(2)+...+α(n)a(n)=0, where a(1), a(2),..., a(n) are columns of A. Now suppose that B is the matrix obtained from A by performing row operations: Show that α(1)b(1)+α(2)b(2)+...+α(n)b(n)=0, where b(1), b(2),..., b(n) are columns of B. Show that the converse is also true.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT