Hello everyone, i need with an exercise about summations, why p + (p + 1) + + (q - 1) + q can be resolved bye the equation .

i just want to know why the summation can be resolved by this equation.

Let denote the sum in question:



Reorder the terms as



Note that each corresponding term in the sums add to :



and so on.

So adding both sums together gives



There are instances of . ( is the difference between the first and last terms of the sum, i.e. the number of terms after to count up to . Adding 1 will include in the count.) So,

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