Răspuns:
2(2²⁰ - 1)
Explicație pas cu pas:
[tex]S = {2}^{1} + {2}^{2} + ... + {2}^{20} [/tex]
[tex]2 \cdot S = 2 \cdot S({2}^{1} + {2}^{2} + ... + {2}^{20})[/tex]
[tex]2 \cdot S = {2}^{2} + {2}^{3} + ... + {2}^{21}[/tex]
[tex]2 \cdot S + 2 = 2 + {2}^{2} + {2}^{3} + ... + {2}^{20} + {2}^{21} \\ [/tex]
[tex]2 \cdot S + 2 = S + {2}^{21}[/tex]
[tex]2 \cdot S - S = {2}^{21} - 2 \implies S = {2}^{21} - 2 \\ [/tex]
[tex] \iff \bf S = 2({2}^{20} - 1)[/tex]
