Question

2) Tìm số dư khi chia A cho 7 biết rằng:
A = 1+2+2^2+ …+ 2^195+ 2^196.

Answer 1

\(A=1+2+2^2+...+2^{195}+2^{196}\)

\(A=\)\(\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{194}+2^{195}+2^{196}\right)+1\)

\(A=2.\left(1+2+4\right)+2^4.\left(1+2+4\right)+...+2^{194}.\left(1+2+4\right)+1\)

\(A=2.7+2^4.7+...+2^{194}.7+1\)

\(A=7.\left(2+2^4+...+2^{194}\right)+1\) 

\(\Rightarrow A\)chia cho 7 dư 1

Answer 2

Cho mình hỏi A=1+2+2^3+2^4+....+2^19

Chứng minh A chia hết cho 3

                        A chia hết cho 5

                        A chia 7 dư bao nhiêu?