6.Efectuați:
[tex]( - 1) + 2 \times ( - 1) {}^{2} + ... + 2019 \times ( - 1) {}^{2019} [/tex]
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Răspuns:
-1010
Explicație pas cu pas:
(-1) + 2·(-1)² + 3·(-1)³+..........+2019·(-1)²⁰¹⁹ =
= (-1)+3·(-1)³+5·(-1)⁵+........+2019·(-1)²⁰¹⁹ + 2·(-1)²+4·(-1)⁴+....+2018·(-1)²⁰¹⁸=
= -1-3-5-.....-2019 + 2+4+6+....+2018 =
= (2-1)+(4-3)+(6-5)+....+(2018-2017)-2019 =
= 1009 - 2019 = -1010
(sunt 2018:2 = 1009 perechi x 1 = 1009)