Question

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Answer 1

$-2\cdot (-1)^n-3\cdot (-1)^{n+1}-5\cdot (-1)^{2n} =\\ \\ =-2\cdot(-1)^n-3\cdot(-1)\cdot (-1)^n-5\cdot \big[(-1)^{2}\big]^n\\ \\ =(-1)^n\cdot \big[-2-3\cdot (-1)\big]-5\cdot 1^n\\ \\ = (-1)^n\cdot (-2+3)-5\\ \\ =(-1)^n\cdot 1-5\\ \\ =\boxed{(-1)^n-5}$