Răspuns:
2²¹ - 2
Explicație pas cu pas:
[tex]S = { | - 2| }^{1} + { | - 2| }^{2} + { | - 2| }^{3} + ... + { | - 2| }^{20} \\ = {2}^{1} + {2}^{2} + {2}^{3} + ... + {2}^{20}[/tex]
[tex]S = {2}^{1} + {2}^{2} + {2}^{3} + ... + {2}^{20}[/tex]
[tex]2S = 2 \cdot ( {2}^{1} + {2}^{2} + {2}^{3} + ... + {2}^{20})[/tex]
[tex]2S + 2 = \underbrace{{2}^{1} + {2}^{2} + {2}^{3} + {2}^{4} + ... + {2}^{20}}_{S} + {2}^{21} \\[/tex]
[tex]2S - S + 2 = {2}^{21} \implies \bf S = {2}^{21} - 2 \\[/tex]
