ITOT 43 Spring 2022 - THPT O - additive practice Question 3

For a positive integer $n$, call $(a_1,\ldots,a_n)$ interesting if $a_i=i$ or $i+1$ for every $i$. Call it even or odd according to the parity of $a_1+\cdots+a_n$. Alice records the product of the entries of every odd interesting sequence; Bob does the same for every even one. Whose recorded numbers have the greater sum, and by how much, as a function of $n$? (5 points)



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