Tentukan hasil dari tanpa menghitung s atu 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

Matematika
Pola Bilangan VII SMP

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

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

————————————————
1 - 2 + 3 - 4 + ... - 100
= (1 - 2) + (3 - 4) + ... + (99 - 100)
= -1 - 1 - 1 - ... - 1
= -(1 + 1 + ... + 1)
= -(100/2)
= -50

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

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

1] menggunakan rumus gaus = ((1 + 99)/2)²
                                                = 50²
                                                = 2.500

2] pengurangan berulang = -100/2
                                         = -50

3] -50 sampai 50 dianggap nol
maka, jumlahkan = -100 - 99 - ..... - 51 → ada 50 bilangan
                            = (50/2) x (-100 - 51)
                            = 25 x (-151)
                            = -3.775