Question

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

Answer 1

Explicație pas cu pas:

c)

$|2| + |5| + |8| + ... + |29| = 2 + 5 + 8 + ... + 29 = (2 + 29) + (5 + 26) + (8 + 23) + (11 + 20) + (14 + 17) = 5 \cdot 31 = 155$

d)

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

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

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

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

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