Question

số dư khi A= 2^0 + 2^1 + 2^2 + ... +2^100 khi chia cho 15

 

Answer 1

 

A= 2^0 + 2^1 + 2^2 + ... +2^100

=2⁰+(2¹+2²+2³+2⁴)+(2⁵+2⁶+2⁷+2⁸)+...+(2⁹⁷+2⁹⁸+2⁹⁹+2¹⁰⁰)

=1+15+2⁵.(1+2+2²+2³)+...+2⁹⁷.(1+2+2²+2³)

=1+15+2⁵.15+....+2⁹⁷.15

=1+15.(1+2⁵+...+2⁹⁷)

Suy ra: số dư khi chia A cho 15 là 1

 

Answer 2

A = (1+2+2^2+2^3)+(2^4+2^5+2^6+2^7)+.....+(2^97+2^98+2^99+2^100)

=15+2^4 .(1+2+2^2+2^3)+.....+2^97.(1+2+2^2+2^3)

=15+2^4.15+....+2^97.15

=15.(1+2+2^2+2^3) :15

Vì 15 chia hết cho 15 

Suy ra 15.(1+2+2^2+2^3) chia hết cho 15

Vậy A chia 15 dư 0

Answer 3

dư 1

tick cho mik nhé bn thân

Answer 4

Nhận thấy 2⁰ + 2¹ + 2² + 2³ =15

2⁰ + 2¹ + 2² + 2³ + 2⁴....+ 2⁹⁷+ 2⁹⁸ + 2⁹⁹ + 2¹⁰⁰

= 1 + (2 + 2² + 2³ + 2⁴) + (2⁵ + 2⁶ + 2⁷ + 2⁸) +...(2⁹⁷+ 2⁹⁸ + 2⁹⁹ + 2¹⁰⁰ )

= 1+ 2 . 15 + 2⁵ .15 + ... + 2⁹⁷.15

= 1 + 15.Q

 Vậy A chia cho 15 dư 1