MathDB
Problems
Contests
National and Regional Contests
Argentina Contests
Argentina National Olympiad
2010 Argentina National Olympiad
5
5
Part of
2010 Argentina National Olympiad
Problems
(1)
v= 2uw/(u+w)
Source: 2010 Argentina OMA Finals L3 p5
1/15/2023
21
21
21
numbers are written in a row.
u
,
v
,
w
u,v,w
u
,
v
,
w
are three consecutive numbers so
v
=
2
u
w
u
+
w
v=\frac{2uw}{u+w}
v
=
u
+
w
2
u
w
. The first number is
1
100
\frac{1}{100}
100
1
, the last one is
1
101
\frac{1}{101}
101
1
. Find the
15
15
15
th number.
algebra