Question

Us=1+2+2²+...+2²⁰²²
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Answer 1

Răspuns:

$s = 1 + \not2 + {\not2}^{2} + .\not.. + {\not2}^{2022} \\ 2s = {\not2} + {\not2}^{2} + {\not2}^{3} + .\not.. + {2}^{2023} \\ \sout{ - - - - - - - - - - - - - }( - )\\ 2s - s = {2}^{2023} - 1 \\\bold{ s = {2}^{2023} - 1}$

Explicație:

2s-s=(2+2²+...+2²⁰²³)-(1+2+2²+...+2²⁰²²)

s=2+2²+...+2²⁰²³-1-2-2²-...-20²⁰²²

• 2-2=0
• 2²-2²=0
• 2³-2³=0
• ....
• 2²⁰²²-2²⁰²²=0
• a rămas doar 2²⁰²³-1