Explicație pas cu pas:
c)
[tex]|2| + |5| + |8| + ... + |29| = 2 + 5 + 8 + ... + 29 = (2 + 29) + (5 + 26) + (8 + 23) + (11 + 20) + (14 + 17) = 5 \cdot 31 = 155[/tex]
d)
[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]
