Question

Efectuati
(3+6+9+......+30)-(2+4+6+.....+20)
*explicati ce teorema ati folosit

Answer 1

3+6+9+...+30  Facem Gauss de fiecare data care zice ca 1+2+3..+n=n (n+1)/
3(1+2+..+10)=  luam paranteza separat

1+2+..+10=10(10+1)/2=
10*11/2=
5*11=55
deci 3*55=165

2+4+6+..+20=
2(1+2+3+..+10) dar am facut mai sus si stim ca da 55

2*55=110

deci 165-110=55

Answer 2

dai factor comun pe 3 in prima paranteza si pe 2 in a doua si vei obtine 3(1+2+3+..+10)-2(1+2+3+...+10)
si folosesti formula 1+2+3+...+n=n(n+1)/2
3*(10*11)supra2-2*(10*11)supra 2=
3*55-2*55=165-110=55