Question

Plssss ajutor chiar am nevoie

Answer 1

19. A₄ = 7 + 7² + 7³ +7⁴  = 7+49 + 343+2401 = 2800

2800 | 2

1400 | 2

700 | 2

350 | 5

70 | 5

14 | 2

7 | 7

1

Deci 2800 = 2⁴ x 5² x 7 - raspuns a)

20. A₂₀₂₀ = 7+ 7² + 7³ +7⁴+7⁵+7⁶+7⁷+.... + 7²⁰²⁰

Grupam termenii cate 4 si dam factor comun convenabil

7(1+7+7²+7³) + 7⁵(1+7+7²+7³) + 7⁸(1+7+7²+7³) + .....+7²⁰¹⁷(1+7+7²+7³) =

7 x 400 + 7⁴ x 400 + 7⁸ x 400 +......+ 7²⁰¹⁷ x 400 =

400(7+7⁵ + 7⁸ + .....+7²⁰¹⁷) =

100x4((7+7⁵ + 7⁸ + .....+7²⁰¹⁷)

Ultimele 2 cifre vor fi 00