Question

Sa se determine x€R pt care 1+4+7.... +x=210

Answer 1

S = (1 + 3×0) + (1 +3×1) + (1 +3×2) + ...+[1 + 3×(n-1)] = 1×n + 3×(1 +2+...+n-1) = n + 3 ×n×(n-1) /2 = [2n + 3n×(n-1)]/2 = n× (2 + 3×(n -1) /2=[ n × (3n -1)]/2= 210 => 3n^2 - n -420 = 0; D = (-1)^2 - 4 × 3 × (-420) = 1 + 5040 =5041; n1,2 = (1 +/- 71)/ 2 × 3 => n1 = 72/6 = 12; n2 = -70/6; x = 1 + (n-1) × 3 = 1 + 3n - 3 = 3n -2; x1 = 12×3 -2 = 34 sau x2 = [3× (-70)/6]- 2 = -74/2 = -37. Sau mai repede cu formulele de la progresii aritmetice: a1 = 1; r=3; an=x= a1 + (n-1) ×r = 1 + (n-1)×3 ; Sn = (a1 + an) ×n /2.