Question

C |+21+|+51 +|+81 +...+|+29|=
d 1-21¹ +1-21²+...+|-2|20 =

Answer 1

Explicație pas cu pas:

d.

$S = { | - 2| }^{1} + { | - 2| }^{2} + { | - 2| }^{3} + ... + { | - 2| }^{20} \\ = {2}^{1} + {2}^{2} + {2}^{3} + ... + {2}^{20}$

$S = {2}^{1} + {2}^{2} + {2}^{3} + ... + {2}^{20}$

$2S = 2 \cdot ( {2}^{1} + {2}^{2} + {2}^{3} + ... + {2}^{20})$

$2S + 2 = \underbrace{{2}^{1} + {2}^{2} + {2}^{3} + {2}^{4} + ... + {2}^{20}}_{S} + {2}^{21}$

$2S - S + 2 = {2}^{21} \implies \bf S = {2}^{21} - 2$