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FullSimplify[(((q^k - 1)(q(-tq^k + 2q - 2) + t))/(4(q - 1))) + (((q^(k+1) - 2q^k + 1)(t(q^(k+1) - 1) - 2q^2 + 2q))/(4(q - 1)^2))]
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