Quiz Math ^_^ Hitunglah [tex] \dfrac{1}{8} + \dfrac{1}{24} + \dfrac{1}{48} + \cdots + \dfrac{1}{10200} [/tex] Petunjuk: 1. Cari pola penyebut 2. Gunakan prinsip

jawab

1/8  = 1/(4.1.2)
1/24 = 1/(4.2.3)
1/48= 1/(4.3.4)
...
1/10.200 = 1/(4)(50)(51)

50
∑  1/(4n(n+1)) 
i = 1

1/4 ( 1/(1.2) + 1/(2.3) + ...+1/(50.51))=
= 1/4(1- 1/2 + 1/2 -1/3 + 1/3 - 1/4 + ...+1/50 -1/51)
= 1/4 (1 - 1/51)
= 1/4 (50/51)
= 25/102