Question

Daca 2 la puterea 2021 × 5 la puterea 2020=a1 a2 a3
...a n care este valoarea sumei S = a1 + a2 +n? VA ROG REPEDE DAU COROANĂ ​

Answer 1

$\red{\large \boxed {\bf S = a_{1} + a_{2}+ n = 2023}}$

Explicație pas cu pas:

Bună

$\large\bf {2}^{2021} \cdot {5}^{2020} = \overline{a_{1}a_{2}....a_{n}}$

$\large \bf \overline{a_{1}a_{2}....a_{n}} = {2}^{2020} \cdot2\cdot {5}^{2020}$

$\large\bf \overline{a_{1}a_{2}....a_{n}} = 2 \cdot(2\cdot 5)^{2020}$

$\large\bf \overline{a_{1}a_{2}....a_{n}} = 2 \cdot10^{2020}$

$\large\bf \overline{a_{1}a_{2}....a_{n}} = 2 \cdot 1 \underset{ 2020 \: zerouri}{\underbrace{000.......00 }}$  

$\large\bf \overline{a_{1}a_{2}....a_{n}} = 2 \underset{ 2020 \: zerouri}{\underbrace{000......00 }}$

$\large\bf \overline{a_{1}a_{2}....a_{n}} = 2 \underset{ 2020 \: zerouri}{\underbrace{000......00 }} \implies 2021~ cifre$

$\bf \large S = a_{1} + a_{2}+ n \implies S = 2 + 0 + 2021 \implies$

$\red{\large \boxed{ \bf \: S = 2023}}$

#copaceibrainly