Very confusing...

Posted by Joel on September 12, 2002 at 09:57:08:

In Reply to: No...because it becomes f(n) after summation (n/t) posted by Subhotosh Khan on September 12, 2002 at 08:02:52:

: : : : Is a Sum statement properly termed a "function"
: : : : so that EITHER of the following:

: : : : f(n) = n(n+1)/2
: : : : and
: : : : f(n) = Sum[from n=1 to n]n

: : : : BY ITSELF would be correctly considered a function that defines the series {1,3,6,10,15...} ?

: : : : The former, of course, is a quadratic function. What is the latter? Is it a propositional function?

: : : You wrote the latter

: : : f(n) = Sum[from n=1 to n]n

: : : wrong

: : : It should be

: : : f(n) = Sum[from j=1 to n]j

: : : Then f(n)= n(n+1)/2

: : : Yes f(n)=n(n+1)/2 defines the series

: : : {1,3,6,10,15...}

: : :

: : Hmmm... now that you pointed it out I agree that
: : f(n) = Sum[from n=1 to n]n
: : seems to have too many n's.

: : But I don't think your f(n) = Sum[from j=1 to n]j looks right either.

: :
: : Shouldn't it be:
: : f(j) = Sum[from j=1 to n]j ?

So, is this a more general (and correct) way to express this type of relationship:

f(n) = Sum[from j=1 to n](f(j))
and in the specific case we were discussing, f(j) happened to be simply j?

Follow Ups:

• Re: Very confusing... T.Gracken 13:42:44 09/12/02 (2)
  • ah, recursion ... Joel 17:48:47 09/12/02 (1)
    • Re: ah, recursion ... T.Gracken 21:34:08 09/12/02 (0)
• keep after 'em, Joel....I'm learning too! I automatically get nervous every time I see the "sigma summation formula" ! Denis Borris 10:59:23 09/12/02 (0)

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