Question

tìm số dư khi chia M cho 13 biết rằng M=1+3+3^2+3^3+3^4+...+3^98+3^99+3^100

Answer 1

M=1+3+3²+3³+3⁴+...+3⁹⁸+3⁹⁹+3¹⁰⁰

M=(1+3+3²)+(3³⁺3⁴+3⁵)+...+(3⁹⁸+3⁹⁹+3¹⁰⁰)

M=(1+3+3²)+3³(1+3+3²)+...+3⁹⁸(1+3+3²)

M=13+3³.13+...+3⁹⁸.13

M=13(1+3³+...+3⁹⁸) chia hết cho 13

=> M chia cho 13 dư 0

Vậy M chia cho 13 dư 0

Answer 2

sai rồi bạn

Answer 3

M có 101 số

M=1+3+3^2+.....+3^100

M=(1+3+3^2)+(3^3+3^4+3^5)+......+(3^96+3^97+3^98)+3^99+3^100

M=13+3^3.(1+3+3^2)+...+3^96.(1+3+3^2)+3^99+3^100

M=13.1+3^3.13+.......+3^96.13+3^99+3^100

M=13.(1+3^3+...+3^96)+3^99+3^100

=>M:13 dư 3^99+3^100

Vậy M:13 dư 3^99+3^100