Question

E=1 3 3^2 3^3 ... 3^1991 chứng minh E chia hết cho 41

Answer 1

B=1+3+\(3^2\)+\(3^3\)+....+\(3^{1991}\)

B=1+3+\(3^2\)+\(3^3\)+....+\(3^{1991}\)

=(1+3+\(3^2\)+\(3^3\))+(\(3^4\)+\(3^5\)+\(3^6\)+\(3^7\))+.....+(\(3^{1988}\)+\(3^{1989}\)+\(3^{1990}\)+\(3^{1991}\))

=(1+\(3^4\))(1+3+\(3^2\)+\(3^3\))(\(3^8\)+....+\(3^{1988}\))

=82.(1+3+\(3^2\)+\(3^3\))(\(3^8\)+....+\(3^{1988}\))

Vì 82⋮41

→E⋮41

→B⋮41(đpcm)

Answer 2

Bạn tham khảo nha: 

B=1+3+32+33+....+31991B=1+3+32+33+....+31991

=(1+3+32+33)+(34+35+36+37)+.....+(31988+31989+31990+31991)=(1+3+32+33)+(34+35+36+37)+.....+(31988+31989+31990+31991)

=(1+3+32+33)+34(1+3+32+33)+....+31988(1+3+32+33)=(1+3+32+33)+34(1+3+32+33)+....+31988(1+3+32+33)

=(1+3+32+33)+(1+34+....+31988)=(1+3+32+33)+(1+34+....+31988)

=(1+34)(1+3+32+33)(38+....+31988)=(1+34)(1+3+32+33)(38+....+31988)

=82.(1+3+32+33)(38+....+31988)=82.(1+3+32+33)(38+....+31988)

Vì 82⋮4182⋮41

→82.(1+3+32+33)(38+....+31988)⋮41→82.(1+3+32+33)(38+....+31988)⋮41

→B⋮41(đpcm)