barisan yang aneh

Posted: October 6, 2010 in matematika, math games

coba amati barisan tak terbatas berikut
1 - 1 + 1 - 1 + 1 -1 + ...
ayo kita bermain”

ada satu kondisi seperti ini
(1 - 1) + (1 - 1) + (1 - 1) + ...
0 + 0 + 0 + .... = 0

dan juga bisa seperti ini
1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ...
1 + 0 + 0 + 0 + 0 + 0 + ...  = 1

yang lebih aneh kalau begini
A = 1 -1 + 1 - 1 + 1 - 1 +  ...
A = 1 -(A) latex A+A = 1 $ 2A =1
A = \frac{1}{2}
malah jadi setengah ? hahaha

bagai mana kalau kita ganti angka nya menjadi

A = 2 -2 + 2 - 2 + 2 - 2 +  ...
A = 2 -(A) latex A+A = 2 $ 2A =2
A = 1

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