A=2+22+23+....+299+2100
A=(2+22+23+24+25)+(26+27+28+29+210)+......+(296+297+298+299+2100)
A=(2+22+23+24+25)+25.(2+22+23+24+25)+....+295.(2+22+23+24+25)
A=62+25.62+.....+295.62
A=62.(1+25+.....+295)
A=31.2.(1+25+...+295)\(⋮\)31
Vậy A\(⋮\)31
Chúc bn học tốt
A=2+2^2+2^3+...+2^100
=(2+2^2+2^3+2^4+2^5)+(2^6+2^7+2^8+2^9+2^10)+....+(2^96+2^97+2^98+2^99+2^100)
=62+2^5(2+2^2+2^3+2^4+2^5)+....+2^95(2+2^2+2^3+2^4+2^5)
=62+2^5.62+2^10.62+....+2^95.62
=62(1+2^5+2^10+...+2^95)
Vì 62 chia hết cho 31 => A chia hết cho 31
Bài làm
Ta có:
A = 2 + 22 + 23 + ... + 299 + 2100
A = ( 2 + 22 + 23 + 24 + 25 ) + ( 26 + 27 + 28 + 29 + 210 ) + ... + ( 296 + 297 + 298 + 299 + 2100 )
A = 2( 1 + 2 + 22 + 23 + 24 ) + 26( 1 + 2 + 22 + 23 + 24 ) + ... + 296( 1 + 2 + 22 + 23 + 24 )
A = 2( 1 + 2 + 4 + 8 + 16 ) + 26( 1 + 2 + 4 + 8 + 16 ) + ... + 296( 1 + 2 + 4 + 8 + 16 )
A = 2 . 31 + 26 . 31 + ... + 296 . 31
A = 31( 2 + 26 + ... + 296 )
Mà \(31⋮31\)
=> \(31\left(2+2^6+...+2^{96}\right)⋮31\)
Vậy \(A=2+2^2+2^3+...+2^{99}+2^{100}⋮31\)
# Học tốt #
