a) 1+2+3+... +80 =
= [80·(80+1)]/2
= (80·81)/2
= 40·81
= 3240
b) 2+4+6+...+100 =
= 2·(1+2+3+...+50)
= 2·[50·(50+1)]/2
= 50·(50+1)
= 50·51
= 2550
c) 1+3+5+...+99 =
= 1+3+5+...+(2·50-1)
= 50²
= 2500
d) 3+7+11+15+...+43 =
= (4·1-1)+(4·2-1)+(4·3-1)+...+(4·11-1)
= 4·(1+2+3+...+11) -1-1-1-...-1 {de 11 ori}
= 4·[11·(11+1)]/2 - 11
= 4·(11·12)/2 - 11
= 4·11·6 - 11
= 11·(24-1)
= 11·23
= 253
