Question

Fie secventa de numere naturale 11,12,13,14,101.Determina cate numere are secventa.Calculeaza s=11+12+13+...+101

Answer 1

Calculam cate numere sunt in sir:
(101 - 11) + 1 = 90 + 1 = 91

Calculam suma:
S = 11 + 12 + 13 +...+ 101
S = (11 + 101) × 91 : 2
S = 112 × 91 : 2
S = 56 × 91
S = 5 096

sau un alt mod de rezolvare:
S = (1+2+3+...+101) - (1+2+3+...+10)
S = 101 × 102 : 2 - 10 × 11 : 2
S = 101 × 51 - 5 × 11
S = 5 151 - 55
S = 5 096

Answer 2

s=1+2+3+...+10+11+12+...+101-(1+2+3+...+10)

s=101×102:2-10×11:2
s=101×51-11×5
s=5.151-55
s=5.096