Question

2+6+10+14+...+30=2*x^3

Answer 1

2 + 6 + 10 + 14 + ...... + 30 = 2 × x³

2 × ( 1 + 3 + 5 + 7 + ..... + 15 ) = 2 × x³

1 + 3 + 5 + 7 + ..... + 15 = 8 × ( 1 + 15 ) : 2 = 4 × 16 = 64

→ stabilesc cati termeni are suma cu ratia 2

( 15 - 1 ) : 2 + 1 = 14 : 2 + 1 = 8 termeni are suma

→ aplic formula sumei lui Gauss

2 x³ = 2 × ( 1 + 3 + 5 + 7 + ..... + 15 )

2 x³ = 2 × 64 = 2 × 2⁶

2 x³ = 2 × 2⁶  l :  2

x³ = ( 2² ) ³ ⇒   x³ = 4³  ⇒   x = 4