I am trying to prove the equation for any integer (k) greater or equal to 0, that 2^(k+1) < (k+3)! I am not sure how to expand the factorial to show that the equation will always be true? Any Help Would Be Greatly Appreciated
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Originally Posted by doleary22 I am trying to prove the equation for any integer (k) greater or equal to 0, that 2^(k+1) < (k+3)! I am not sure how to expand the factorial to show that the equation will always be true? Any Help Would Be Greatly Appreciated If we write... (1) (2) ... You observe that the product (2) has k+2 factors and the product (1) k+1 factors and for i=1,2,...,k+1 is , so that the conclusion is obvious... Kind regards
I am still a little confused because I am not familiar with the notation. Is there any other way to solve the problem?
Originally Posted by doleary22 I am still a little confused because I am not familiar with the notation. Is there any other way to solve the problem? A more elementary concept probably doesn't exist... (1) (2) Do You understand now?... Kind regards
I understand how to solve each side of the equation, but what I am confused about is how did you determine the factors in your first response, and then how do I compare those two products to show that the one will always be larger than the other?
Hello, doleary22! Here is an observation. I hope you can modify it into a proof. . . . . . . . . .
I am still a little confused. I know that the statement is correct, but I just can't seem to wrap my head around a logical way to write down a proof.
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