Posted by Denis Borris on September 12, 2002 at 10:59:23:
In Reply to: Very confusing... posted by Joel on September 12, 2002 at 09:57:08:
: : : : : 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?