Question

Số dư của 2^0+2^1+2^2+2^3+...+2^100 khi chia cho 15

Answer 1

2^0 + 2^1 + 2^2+  2^3 + ..... +2^100

= (2^1+2^2+2^3+2^4) + ... + (2^97 + 2^98 + 2^99 + 2^100) + 1

= 2.15 + 2^5.15+...+2^97.15 + 1

= 15.(2+2^5+...+2^97) + 1

Chia 15 dư 1 

Answer 2

 

2^0+2^1+2^2+2^3+...+2^100

=1+(2¹+2²+2³+2⁴)+.....+(2⁹⁷+2⁹⁸+2⁹⁹+2¹⁰⁰)

=1+2.(1+2+2²+2³)+....+2⁹⁷.(1+2+2²+2³)

=1+2.15+....+2⁹⁷+15

=1+15.(2+...+2⁹⁷)

=>số dư là 1