Question

Suppose that m and n are positive integers with m 2 2. the (m, n)-sawtooth sequence is a sequence of consecutive integers that starts with 1 and has n teeth, where each tooth starts with 2, goes up to m and back down to 1. for example, the (3, 4)-sawtooth sequence is
the (3, 4)-sawtooth sequence includes 17 terms and the average of these terms is 3.
(a) determine the sum of the terms in the (4,2)-sawtooth sequence.
(b) for each positive integer m 2 2, determine a simplified expression for the sum of the ter in the (m, 3)-sawtooth sequence.
(c) determine all pairs (m, n) for which the sum of the terms in the (m, n)-sawtooth sequence is 145.
(d) prove that, for all pairs of positive integers (m, n) with m≥ 2, the average of the terms in the (m, n)-sawtooth sequence is not an integer.

Answer 1

Answer:

Narendra Singh Rajawat