User talk:JBL
For later use (Mock AIME 2006)
Let the ratio of consecutive terms of the sequence be . Then we have by the given that
so
and
, where
can be any of the tenth roots of unity.
Then the sum has value
. Different choices of
clearly lead to different values for
, so we don't need to worry about the distinctness condition in the problem. Thus our final answer will be
.
For every choice of ,
is also a 10th root of unity, so if we take 2 copies of
we can pair up terms to get
About CMO
I am sorry about CMO. What do you suggest I should do? Redirect? Recreate the pages? By the way "Cyprus Mathematical Olympiad" it is the official translation. The papers are in both English and Greek.