Question

Sa se determine care pot fi ultimele 2 cifre ale sumei a 25 numere consecutive.
Coroana!!!!!!!!!!!!!!!!!!!!!!

Answer 1

1+ 2+ 3+ ....+ 25= (25x 26):2= 25x 13= 325;S= 11+ 12+ 13+ ...+ 35 sunt 25 de numere ( 35-11+ 1) ; S = 35+ 34+ ....+ 11; adunam una sub alta si vom avea 2S = 46+ 46+ ...+ 46= 46x 25= 1150 ; S = 1150:2= 575 ; n + ( n+1) + ( n+2) + ....+( n+24) = 25n + 1+ 2+ 3+ ...+ 24= 25n + (24x 25):2= 25n + 12x 25= 25n + 300; pt n= 1 vom avea 25+ 300= 325; n= 2, vom avea 50+ 300= 350 ; n= 3, 75+ 300= 375; n=4 , 100+ 300= 400; n= 5 , 125+ 300= 425; n= 6, 150+ 300= 450 ; n= 7, 175+ 300= 475; concluzie ultimele doua cifre vor fi : { 00, 25, 50, 75, }