Question

tentukan hasil dari (tanpa menghitung satu persatu)
a. 1+3+5+7+9+...+99
b. 1-2+3-4+5-6+7-8+...-100
c. -100-99-98-...-2-1-0+1+2+...+48+49+50

Answer 1

Mapel : Matematika
Kelas : IX SMP
Bab : Barisan dan deret

Pembahasan :
Un = 2n - 1
99 = 2n - 1
2n = 100
n = 50

1 + 3 + 5 + 7 + ... + 99 = n²
1 + 3 + 5 + 7 + ... + 99 = 50²
1 + 3 + 5 + 7 + ... + 99 = 2500

————————————————
1 - 2 + 3 - 4 + ... - 100
= -1 - 1 - 1 - 1 - ... - 1
= -(1 + 1 + ... + 1)
= -(100/2)
= -50

————————————————
Un = 50
a + (n - 1)b = 50
-100 + n - 1 = 50
n - 101 = 50
n = 151

-100 - 99 - 98 - ... + 50
= S151
= 151/2(-100 + 50)
= 151/2(-50)
= -3775

Answer 2

Materi Baret

a) 1 + 3 + 5 + ... + 99 = (1 + 99) + (3 +97) + ... + (49+51) = 100 × 25 = 2500
b) 1 - 2 + 3 - 4 + ... - 100 = (1-2)+(3-4)+(5-6)+...+(99-100) = -1 × (50) = -50
c) -100 - 99 - 98 - .... + 50 = -100 - 99 - ... - 51
= (-100 - 51) + (-99 - 52) + ... + (-76 - 75) = 25 × -151 = -3775