tentukan hasil dari(tanpa menghitung satu persatu) no 7

Materi : Teori Bilangan

Pembahasan :
Un = 100
2n = 100
n = 50

2 + 4 + 6 + ... + 2n = n(n + 1)
2 + 4 + 6 + ... + 100 = 50(50 + 1)
2 + 4 + 6 + ... + 100 = 50(51)
2 + 4 + 6 + ... + 100 = 2550

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

————————————————
Un = 99
a + (n - 1)b = 99
-100 + (n - 1)1 = 99
-100 + n - 1 = 99
n - 101 = 99
n = 200

-100 - 99 - 98 - ... + 99
= n/2(a + Un)
= 200/2(-100 + 99)
= 100(-1)
= -100