Ta có :
5+52+53+...+5100
= (5+52) + (53+54)+...+(599+5100)
= (5+52) + 52(5+52) +....+598(5+52)
= 30 + 52.30+...+598.30
=30(1+52+...+598) chia hết cho 30
Vậy 5+52+53+...+5100 chia hết cho 30
dễ:
5 + 52 + 53 + ....... + 5100
= ( 5 + 52 ) + ( 53 + 54 ) + ............+ (599 + 5100)
= 30 + 53( 5 + 52 ) + ........... + 599( 5 + 52 )
= 30 + 53 . 30 + ........... + 599 . 30
= 30( 53 + ..........+. 599 ) chia hết cho 3