proof

I got the RHS of the inequality just dont understand why 1 is less than nth root of n. Should it not be less than or equal to?

Is this how I should complete my proof: By way of contradiction assume that 2k is the largest even integer. Now consider (2k)! (2k)! = (2k)(2k-1)(2k-2).......(k)(k-1)(k-2)......(2)(1) = 2[k(2k-1)(2k-2).......(k)(k-1)(k-2)......(2)(1)] = 2p, which is also an even integer. This contradicts...

The question was asking: Prove the following statement using either direct or contrapositive proof: If n is an integer then 4 does not divide n^2-3 Here is my working out: let n^2 - 3 = 4m By way of contradiction assume n^2 - 3 is rational, ie; n^2 - 3 = a/b (BTW in the funky looking...

I have come across some questions that are asking me to prove the general formula for a certain sequence. I do now know how to tackle these questions. Can someone please tell me how to do them? Here is a problem from the question set that appeared: A sequence is given by the first order...

For the following question when I am trying to prove the n = k+1 case am I allowed to substitute it in the first line of the question and also in the second line of the question? What I am trying to say is am i allowed to assume:

I am really confused for the following proof question and am unsure where to start (I don't really get the hint) I would really appreciate it if anyone helped me out with this question

I am just wondering if anyone can have a look at my solution to the following proof question: Question: "Prove by contradiction that there exists no 'n' that is an element of the natural numbers, such that n^2 + 2 is divsible by 4" My Solution: By way of contradiction assume their exists...

RTP: 2^n + 3^n =/= 5^n is it possible to do by induction? any help appreciated thanks

hey all, found this hard proof question, can anyone help me thanks in advance

hey all, need a bit of help with this question thanks in advance.