Question

S=28+30+32+34+...+544
S=33+36+39+...+80
S=2+5+8+...+602

S=2+8+14+...302
rezolvarea este prin rati!!!!!!!!!!!!!!

Answer 1

S = 28 + 30 +.....+ 544  = 2+4+6+....+26 +28+30+....+544-(2+4+6+......+26) =
= 2(1+2+3+......+272 ) - 2(1+2+3+....+13) = 2·272·273/2 - 2·13·14/2 =
= 272·273 - 13·14 = 26(2856 - 7) = 26·2849 = 74074
S = 33+ 36+....+90  = 3+ 6+ 9+.....+30 +33 + 36 +....+90 -(3+ 6+9+....+30) =
= 3(1+2+3+.....+30) - 3(1+2+3+....+10) = 3·30·31/2 - 3·10·11/2 =
= 3·10/2 (93 - 11) = 15·82 = 1230
S = 2 + (2 + 3·1) + ( 2+ 3·2) + (2 +3·3)+ ......+(2 + 3·200) =
= 2·201 +3(1+2+3+....+200) = 2·201 +3·200·201/2 =2·201(1+150) = 60702
S = 2 +(2 +6·1) + (2+6·2) +.......+(2+6·50) = 2·51+6(1+2+........+50) =
= 2·51 + 6·50·51/2 = 2·51(1 + 75) = 7752