Question

cho B= 1+ 5+ 5^2+ 5^3+ ... + 5^96+ 5^97+ 5^98 chứng tỏ B chia hết cho 31

Answer 1

B= 1+ 5+ 5^2+ 5^3+ ... + 5^96+ 5^97+ 5^98

=(1+5+5²)+(5³+5⁴+5⁵)+....+(5⁹⁶+5⁹⁷+5⁹⁸)

=31+(5³.1+5³.5+5³.5²)+....+(5⁹⁶.1+5⁹⁷.5+5⁹⁸.5²)

=31+5³.(1+5+5²)+....+5⁹⁶.(1+5+5²)

=31.1+5³.31+...+5⁹⁶.31

=31.(1+5³+...+5⁹⁶)

=> B chia hết cho 31

 

Answer 2

B = 1+5+5²+5³+....+5⁹⁸

B = (1+5+5²)+(5³+5⁴+5⁵)+....+(5⁹⁶+5⁹⁷+5⁹⁸)

B = 1(1+5+5²)+5³(1+5+5²)+....+5⁹⁶(1+5+5²)

B = 1.31 + 5³.31+.......+5⁹⁶.31

B = 31.(1+5³+.....+5⁹⁶) chia hết cho 31 (đpcm)

Answer 3

B = 1+5+52+53+....+598

B = (1+5+52)+(53+54+55)+....+(596+597+598)

B = 1(1+5+52)+53(1+5+52)+....+596(1+5+52)

B = 1.31 + 53.31+.......+596.31

B = 31.(1+53+.....+596) chia hết cho 31 (đpcm)