Question

|-2|¹+|-2|²+...+|-2|²⁰=​

Answer 1

Răspuns:

2²¹ - 2

Explicație pas cu pas:

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

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

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

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

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

Answer 2

l-2|¹+|-2|²+...+|-2|²⁰=S

modul lui ±2 este valoarea absolută=2

S=2+2²+2³+...+2¹⁹+2²⁰

2S=2²+2³+2⁴+...+2²¹±2

2S=(2+2²+2³+2⁴+...2²⁰)+2²¹-2

2S+2=S+2²¹

S=2²¹-2