Question

chứng minh rằng A = 21^9+21^8+21^7+....+21+1 SOS

Answer 1

Chứng minh gì em?

Answer 2

*) A = 21⁹ + 21⁸ + 21⁷ + ... + 21 + 1

= (21⁹ + 21⁸) + (21⁷ + 21⁶) + ... + (21 + 1)

= 21⁸.(21 + 1) + 21⁶.(21 + 1) + ... + 22

= 21⁸.22 + 21⁶.22 + ... + 22

= 22.(21⁸ + 21⁶ + ... + 1)

= 2.11.(21⁸ + 21⁶ + ... + 1) ⋮ 2

Vậy A ⋮ 2

*) A = 21⁹ + 21⁸ + 21⁷ + ... + 21 + 1

= (21⁹ + 21⁸ + 21⁷ + 21⁶ + 21⁵) + (21⁴ + 21³ + 21² + 21 + 1)

= 21⁵.(21⁴ + 21³ + 21² + 21 + 1) + 204205

= 21⁵.204205 + 204205

= 204205.(21⁵ + 1)

= 5.40841.(21⁵ + 1) ⋮ 5

Vậy A ⋮ 5