On the elimination method of split term What is the basis for the sum of the split term elimination method? How does the equation hold

The basis is: the reciprocal sequence of the product of two equidistant terms in the arithmetic sequence can be summated by the split term elimination method, such as: 1 / N * (n + 1) 1 / (2n-1) * (2n + 1) 1 / an * a (n + 1) 1 / an * a (n + k) how to split 1 / an * a (n + k) method: the inverse method: split the general term of the sequence into 1 / an-1 / a (n + k) = (a (n + k) - an) / [an * a (n + k)]

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