Thank you so much ! :)
On Fri, Nov 6, 2009 at 11:00 AM, Prunthaban Kanthakumar <
pruntha...@gmail.com> wrote:
> On a related note,
> The solution I gave you is to find the nth element in the kth series.
> If you want to sum the first 'n' elements of the kth series (call the
> function s(n,k)), then it is easy to see that,
>
> *s(n,k) = f(n+1, k+1) - 1*
>
> where f(n+1, k+1) is the (n+1)th element in the (k+1)th series.
> This can also be easily done using the summation operator of 'finite
> calculus'.
>
>
> On Fri, Nov 6, 2009 at 10:50 AM, Prunthaban Kanthakumar <
> pruntha...@gmail.com> wrote:
>
>> This is a 'finite calculus' (differences & summations) problem.
>> You can solve it using difference operator (actually its inverse which
>> gives you the discrete integration which is nothing but summation).
>> If you do not know finite calculus, Google for it (or refer Concrete
>> Mathematics by Knuth).
>>
>> The solution for any k is.
>>
>> *f(n) = nC(k+1) + nC(k-1) + nC(k-3) + .... (all the way down to nC0 or
>> nC1 depends on k is odd or even).*
>>
>> Here nCr is the binomial coefficient "n choose r".
>>
>> Eg: Let k = 3, n = 4
>>
>> f(4) = 4C4 + 4C2 + 4C0 = 1 + 6 + 1 = 8
>>
>> Another, k = 3 and n = 5
>>
>> f(5) = 5C4 + 5C2 + 5C0 = 5 + 10 + 1 = 16
>>
>>
>> On Wed, Nov 4, 2009 at 11:23 AM, abhijith reddy <abhijith200...@gmail.com
>> > wrote:
>>
>>> Is there a way to find the sum of the Kth series ( Given below)
>>>
>>> K=0 S={1,2,3,4,5,6,....}
>>> K=1 S={1,2,4,7,11,16..} common diff = 1,2,3,4 5 ...
>>> K=2 S={1,2,4,8,15,26...} common diff = 1,2,4,7 11... (series with
>>> K=1)
>>> K=3 S={1,2,4,8,16,31...} common diff = 1,2,4,8 15... (series with
>>> K=2)
>>>
>>> Note that the common difference of Kth series is the (K-1) series
>>>
>>> Any ideas ??
>>>
>>> --
>>>
>>> You received this message because you are subscribed to the Google Groups
>>> "Algorithm Geeks" group.
>>> To post to this group, send email to algoge...@googlegroups.com.
>>> For more options, visit this group at
>>> http://groups.google.com/group/algogeeks?hl=en.
>>>
>>>
>>>
>>
> --
> You received this message because you are subscribed to the Google Groups
> "Algorithm Geeks" group.
> To post to this group, send email to algoge...@googlegroups.com.
> For more options, visit this group at
> http://groups.google.com/group/algogeeks?hl=en.
>
--
You received this message because you are subscribed to the Google Groups
"Algorithm Geeks" group.
To post to this group, send email to algoge...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/algogeeks?hl=en.
