Question

calculati sumele : a. S=15+16+17+....296 b.2+7+12+....502 c.S=11+22+33+.....+99 d. S= 111+222+333+...+999
DAU COROANA!!!! si 50 puncte

Answer 1

a)
S = 15+16+17+...+296
S = (1+2+3+...+296) - (1+2+3+...+14)
S = 296 × 297 : 2 - 14×15:2
S = 148×297 - 7×15
S = 43 956 - 105
S = 43 851

b)
S = 2+7+12+...+502
S = 5×1-3 + 5×2 - 3 + 5×3-3 +...+ 101×5-3
S = 5×(1+2+3+...+101) - (3+3+3+...+3) de 101 ori
S = 5 × 101 × 102 : 2 - 3 × 101
S = 505 × 51 - 303
S = 25 755 - 303
S = 25 452

c)
S = 11 + 22 + 33 + ... +99
S = (99 + 11) × 9 : 2
S = 110 ×9 : 2
S = 55 × 9
S = 495


d)
S = 111 + 222 + 333 +...+ 999
S = 111×(1 + 2 + 3 +...+ 9)
S = 111 × 9 × 10 : 2
S = 111 × 9 × 5
S = 4 995