Question

Daca 2+6+10+14+...+30=2*x la 3 ,atunci x este:
A.impar
B.patrat perfect
C.par si diferit de 4
D.cub perfect

Answer 1

2+6+10+14+......+30=2·x³
2=4·0+2
6=4·1+2
10=4·2+2
14=4·3+2
......
30=4·7+2
2+6+10+14+.......+30=
4·0+2+4·1+2+4·2+2+4·3+2+.......+4·7+2=
4(1+2+3+......+7)+2·8=
4·7·4+16=
16·7+16=16·8=128
Deci 128=2·x³⇒x³=64⇔x³=4³⇔x=4;
In concluzie ,varianta corecta este:
b. patrat perfect deoarece 4=2².