Question

Calculați: a=(-1)^n•(-2)+(-1)^n+2•3-(-1)^2n+3•(-4),n aparține lui N.

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Answer 1

$a=(-1)^n\cdot(-2)+(-1)^n+2\cdot3-(-1)^{2n}+3\cdot(-4) \\ 1.n=2k,k~apartine~lui~Z \\ a=(-1)^{2k}\cdot(-2)+(-1)^{2k}+2\cdot3-(-1)^{2\cdot2k}+3\cdot(-4) \\ a=1+(-2)+1+2\cdot3-1+3\cdot(-4) \\ a=1+(-2)+1+6-1+(-12) \\ a=(-1)+1+6-1+(-12) \\ \boxed{a=-7} \\ 2.n=2k+1,k~apartine~~lui~Z \\ a=(-1)^{2k+1}\cdot(-2)+(-1)^{2k+1}+2\cdot3-(-1)^{2\cdot2k+1}+3\cdot(-4) \\ a=(-1)\cdot(-2)+(-1)+2\cdot3-(-1)+3\cdot(-4) \\ a=2+(-1)+6-(-1)+(-12) \\ \boxed{a=-4}$