Given an integer n (n≠0), there are a finite number of sequences of consecutive integers whose terms add up to n (If n=25, then 3+4+5+6+7=25 is one such sequence with 5 terms).

a. Find an equation for the number of terms of the longest such sequence for any positive integer n.

b. Find equations for the bounds (the first and last terms) of the longest such sequence for any positive integer n.

Hint: Once you have an equation for the number of terms, and for the first term of the sequence, the last term is simply one less than their sum.

Hint 2: Ducks have absolutely nothing to do with the problem.

Assuming that the sequence does not restrict itself to just positive integers, my solutions are:
A) the number of terms will be 2n, if the series extends from -(n-1) to n
b) the bounds will thus be -(n-1) and n

Example: if the integer is 587, the sequence will be -586+(-585)+(-584)...+587

Posted by H on 2003-08-04 16:43:28