Question

Va rog da m-a ajutati ! Calculati următoarele sume :
A) 1+2+3+.............+80
B) 2+4+6+...................+100
C)1+3+5+...................+90
D)3+7+11+15+..........+43.

Answer 1

A) 1+2+3+............+80 = 80·81/2 = 3240

B) 2+4+6+ ...........+100= 2(1+2+3+.......50) = 2·50·51/2 =2550

C) 1= 1+2·0

     3= 1+2·1

     5= 1+2·2

......89=1+2·44   ⇒ 1+3+5+......89 = 1·45 +2·44·45/2 =2025

1+3+5+........90 =2025+90 = 2115

D 3= 3+4·0

    7=3 +4·1 

   11=3+4·2

.....43 =3+4·10 ⇒ S = 3·11 + 4·10·11/2 =33+ 220 = 253