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expand 1/4 ((k+1/2)^4 - (k-1/2)^4) - 1/8((k+1/2)^2 - (k-1/2)^2) - ((k+1/2)^3 - (k-1/2)^3)
expand 1/4 ((k+1/2)^4 - (k-1/2)^4) - 1/8((k+1/2)^2 - (k-1/2)^2) - ((k+1/2)^3 - (k-1/2)^3)
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