Question

BT1:Cho A=3+3³+3⁵+......+3¹⁹⁹¹

CMR: A chia hết cho 41

BT2:Cho B=4+4²+4³+........+4²⁴

CMR: a)B chia hết cho 20

b)B chia hết cho 21

c)Bchia hết cho 420

Answer 1

Bài 1:

\(A=3+3^3+3^5+3^7+...+3^{1991}\)

\(A=\left(3+3^3+3^5+3^7\right)+....+\left(3^{1985}+3^{1987}+3^{1989}+3^{1991}\right)\)

\(A=\left(3+3^3+3^5+3^7\right)+...+\left(3+3^3+3^5+3^7\right)3^{1985}\)

\(A=\left(3+3^3+3^5+3^7\right)\left(1+....+3^{1985}\right)\)

\(A=2460.\left(1+.....+3^{1985}\right)\)

Vì 2460 chia hết cho 41 nên A chia hết cho 41(đpcm)

Chúc bạn học tốt!!!