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in two different ways:
:
:Rewriting the terms in reverse order:
:

Adding the corresponding terms of both sides of the two equations and halving both sides:
:This formula can be simplified as:
:Furthermore, the mean value of the series can be calculated via: :
:

The formula is essentially the same as the formula for the mean of a discrete uniform distribution, interpreting the arithmetic progression as a set of equally probable outcomes.

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