Recent content by mathstime

how do I evaluate \sum_{k=0}^d \binom{n+d-k}{n} ?

anyone??

Ok, I can now successfully work through that answer - thank you for you help. I just have one question remaining. Why can we not show that it is equal to \binom{n+d}{n} in this way??

I get that this equals \binom{n+d+1}{n} + \binom{n+d+1}{n+1} = \binom{n+d+2}{n+1} is this correct? If so, how can I show that this equals \binom{n+d}{n} ??

Yes, you are correct. The summation should be from 0 to d. I have actually altered the problem slightly. I want to show that \sum_{k=0}^d \binom{n+d-k}{n} = \binom{n+d}{n}?? I could maybe do this by induction on d as follows: d=0 : \binom{n}{n} = \binom{n+1}{n+1} assume true...

got it! thanks!

Hi aracharya Thanks for your input! Your example confuses me a little, but the more I read over it, the more it starts to make sense. Can you summarize what you are doing?? Also, how come you end up with (n-1)'s in your final line? Sorry if I'm just being silly!

I'm sorry I don't understand? Could you explain again? Thank you for your help

Hi I am looking to show that \binom{|\mathbbm{F}| + n -1}{n} = \frac{1}{n!} |\mathbbm{F}|^n + O(|\mathbbm{F}|^{n-1}) please could someone show me how??

Does \sum_{i=0}^n \binom{n-1+d-i}{d-i} = \binom{n+d}{d}??

Thank you, your example helped a great deal

And just to clarify, I am not actually in high school anymore, I have left and been working for some years, but would like to go back to school to study maths, so have been taking some outside classes and reading around a bit. Your help is much appreciated :)

Ramshop, thank you for your help. This problem is still quite confusing to me, but the way you have laid it out is starting to make sense.

That isn't very kind. I thought this site was supposed to encourage learning? If I want to get into university to do a mathematics degree, I need to feel like I can ask for help.

Prove that the number of monomials of degree d in finite field F[x] is \binom{n+d}{n} This is not so much a homework question as something I have read and asked my professor about. He said it was too easy and that I should be able to do it and wouldn't help me. I know I'm probably being a...