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suppose that m and n are …

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suppose that m and n are positive integers with m≥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 3 2 2 3 3 3 2 2 2 2 2 2 1 1 1 1 1 the (3, 4)-sawtooth sequence includes 17 terms and the average of these terms is (a) determine the sum of the terms in the (4, 2)-sawtooth sequence. (b) for each positive integer m ≥2, determine a simplified expression for the sum of the terms 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.
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