Recent content by caseyd1981

Great! I hope I got it right then...I have no clue what a vertical line would imply? Is there such a thing? It seems to me that the object would have to be in 2 positions at the same time, which is impossible. And thanks for your help!

I know this is going to sound easy, but I cannot find the answer anywhere.. We had a quiz today in my physics class, and one of the questions was a True/False question that stated that it is impossible for a position vs time graph of some animal to be perfectly vertical or perfectly...

Alright, let's see. So what I need to prove is (n+1+k)!/(n+1-1)!(k+1) Which, simplified is: (n+1+k)!/n!(k+1) I add (n+1+k-1)!/(n+1-1)! to both sides and this is what my RHS becomes: (n+k)!/(n-1)!(k+1) + (n+1+k-1)!/(n+1-1)! Simplify...

Oh boy, I'm not sure that I follow...??

Oh wow! I see now! Thank you so much for helping me start this one off. One more question, may I ask what is k in this statement? The index is j through n, so what exactly is k?

Give a recursive definition of a) the set of odd positive integers b) the set of positive integer powers of 3 c) the set of polynomials with integer coefficients I have the first two: a) f(0)=1, f(n)=f(n-1)+2 for n>=1 b) f(0)=1, f(n)=3f(n-1) for n>=1 For c, I am not even quite...

I need to prove this by induction and I'm lost on how to even start, help please? Prove that for all positive integers k and n: ∑ j=1 through n, j(j+1)(j+2) . . . (j+k-1) = n(n+1)(n+2) . . . (n+k) / (k+1)

That is it! Thank you all very much. Ok, now I need to prove the formula using induction. Kind of stuck there too...?

Yes, that is correct. I noticed that too but I typed it exactly the way my book did.

This is the last part of the problem and I just can not figure out a formula for it. Here is what the question asks: Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of nonnegative integers to the set of integers. If f is well...