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Products of natural numbers The American Mathematical Monthly

The American Mathematical Monthly


Summary: 1 - We know that the two sequences (Un) and (Vn) defined in N by: Un = 2n and Vn= 2n +1 are two arithmetic sequences and their sums are respectively: Sn =U0+U1+……+Un = n (n +1) and S'n =V0+V1+……. +Vn = (n +1)2 Our modest work is to calculate the product of the terms of these two arithmetic sequences that is to say, to calculate the two following products: P=2×4×6×........ × (2n) and P` =1×3×5×……..× (2n +1) 2 - The concept of the factorial of a natural number will be used to lead to the formulation of the product of the factorial of integers that will be useful in counting and scientific computing.

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