Question

calculati: (6+12+18+24+...+600)la puterea a 2-A : (3+6+9+...+300): (1+2+3+...+100)=

Answer 1

1+2+....+n=[n(n+1)]/2

(1+2+3+...+100)=[100(100+1)]/2=50×101=5050

(6+12+18+24+...+600)²=[6(1+2+.....+100)]²=[6×5050]²

(3+6+9+...+300)=3(1+2+....+100)=3×5050

(6+12+18+24+...+600)² : (3+6+9+...+300): (1+2+3+...+100)=

[6×5050]² : 3×5050 : 5050= 6² : 3 = 36 :3 = 12

Answer 2

( 6 + 12 + 18 + 24 + ......+ 600 )² : ( 3 + 6 + 9 + .....+ 300 ) : ( 1 + 2 + 3 + .....+ 100) =

= 6² ( 1 + 2 + 3 + ,,,,,,+ 100)² : 3 ( 1 + 2 + 3+ .......+ 100 ) : ( 1 + 2 + 3 + .......+ 100 ) =

= ( 36 : 3) ( 1 + 2 + 3 + .......+ 100 ) ⁽ ² ⁻ ¹ ⁻ ¹ ⁾ = 12 ( 1 + 2 + 3+ .......+ 100 )⁰ = 12 × 1 = 12

Raspuns: 12