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First, the answer:

a-sub-n = [2n - 1 - (-1)^n+1]/4.

Now, the reasoning:

Each term = n - (1/n) - (1/2 for odd n's, 0 for even n's).

The formula for the alternating 1/2's and 0's is [1 + (-1)^n+1]/4

Simplification leads to the answer first given above.

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