Răspuns:
[tex]\color{#C41E3A}\Large \boxed {\bf S = a_{1} + a_{2}+ n = 2023}[/tex]
Explicație pas cu pas:
Bună
[tex]\large\bf {2}^{2021} \cdot {5}^{2020} = \overline{a_{1}a_{2}....a_{n}}[/tex]
[tex]\large \bf \overline{a_{1}a_{2}....a_{n}} = {2}^{2020} \cdot2\cdot {5}^{2020}[/tex]
[tex]\large\bf \overline{a_{1}a_{2}.......a_{n}} = 2 \cdot(2\cdot 5)^{2020}[/tex]
[tex]\large\bf \overline{a_{1}a_{2}........a_{n}} = 2 \cdot10^{2020}[/tex]
[tex]\large\bf \overline{a_{1}a_{2}.......a_{n}} = 2 \cdot 1 \underset{ 2020 \: zerouri}{\underbrace{000.......00 }}[/tex]
[tex]\large\bf \overline{a_{1}a_{2}.......a_{n}} = 2 \underset{ 2020 \: zerouri}{\underbrace{000.........00 }}[/tex]
[tex]\large\bf \overline{a_{1}a_{2}....a_{n}} = 2 \underset{ 2020 \: zerouri}{\underbrace{000........00 }} \implies\overline{a_{1}a_{2}....a_{n}} ~~are~ 2021~ cifre[/tex]
[tex]\bf \large S = a_{1} + a_{2}+ n \implies S = 2 + 0 + 2021 \implies[/tex]
[tex]\color{purple}\Large \boxed{ \bf \: S = 2023}[/tex]
PS: Daca esti pe telefon, te rog sa glisezi spre dreapta pentru a vedea rezolvarea completa
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