Question

cum se rezolva a=1-2+3-4+...+21-22
va rog ajutati.ma!!!!!!!

Answer 1

a=1-2+3-4+...+21-22=-1-1-.....-1=-11
22:2=11 grupe a caror suma = -1

Answer 2

1- 2+ 3- 4+ ... +21-22=

1+ 3+ 4+ 5+ ...+ 21- 2- 4- .... -22=

(1+ 3+ 5+ ...+ 21)-( 2+ 4+ 6+ ... + 22)=

[1+ (1+2)- (1+ 4)+...+(1+20)]-(1·2+2·2+3·2+ ...+11·2)=

[(1+1+1...+1)+(2+4+...+20)]-[2·(1+2+3+...+11)]=

[1·11+(1·2+2·2+3·2+ ...+10·2)]-(2·11·12:2)=

[1·11+2·(1+2+3+...+10)]- (11·12)=

(11+2·10·11:2)- (11·12)=

(11·1+10·11)- (11·12)=

[11·(1+10)]- (11·12)=

(11·11)- (11·12)=

11·( 11-12)=

11·(-1)=

-11