Question

cho 2^0+2^1+...+2^100 khi chia cho 15 có số dư là...

Answer 1

Đặt A=2⁰+2¹+2²+...+2¹⁰⁰

  =(2⁰+2¹+2²+2³)+..+(2⁹⁷+2⁹⁸+2⁹⁹+2¹⁰⁰)

  =1.(2⁰+2¹+2²+2³)+...+2⁹⁷.(2⁰+2¹+2²+2³)

  =1.15+...+2⁹⁷.15

  =15.(1+...+2⁹⁷) chia hết cho 15

Vậy A chia 15 dư 0

 

Answer 2

2^ 0 + 2^1 + 2^2+  .... + 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