[Edis]

I need help about sums ,how do i calculate ,,I know the result but how to I get?

[M.M.HUSSAIN]

i wish i could help, but i can't i'm really sorry

[TenOfThem]

Is that a fraction in the bracket

Is it

[Edis]

How then?

[TenOfThem]

(Original post by Edis)
How then?

Is it?

[Ateo]

(Original post by Edis)
I need help about sums ,how do i calculate ,,I know the result but how to I get?

Here's my attempt so far, Ill give it a bit more thought, mind posting the answer so I know where I am heading?





Thats my go however keep in mind that the only knowledge that I have in this is from the binomial expansion. Would be nice if you could post the answer though.

[Edis]

, but why?

[Ateo]

(Original post by Edis)
, but why?

I can't get much else beyond what I wrote. I am sure that this problem is not secondary school level, it would be sixth form at least. Perhaps a better mathematician on the forums here can provide you with a method. I also found the difference between each term of the series you posted to be if its of any use.

[aznkid66]

This isn't a formal proof, but if you do casework for n=1, n=2, n=3, etc. then you find that the summation equals the middle number of every 2n-1^th row in Pascal's Triangle. Thus, it fits the formula "2n-1 choose n-1" (because n is half of 2n).

Maybe a proof by induction will work?

[Edis]

This has nothing to do with the questions, this is the fifth page of the generating function.?

[Ateo]

(Original post by Edis)
This has nothing to do with the questions, this is the fifth page of the generating function.?

I'm sorry about that, I had a quick glance at what was written without actually reading it. Ashamed of that post. I would be keen on seeing a solution to your question myself. Sorry again, don't know what I was thinking.