MathDB
Problems
Contests
National and Regional Contests
Belgium Contests
Flanders Math Olympiad
1993 Flanders Math Olympiad
4
trig product
trig product
Source: flanders '93
September 27, 2005
trigonometry
limit
Problem Statement
Define the sequence
o
a
n
oa_n
o
a
n
as follows:
o
a
0
=
1
,
o
a
n
=
o
a
n
−
1
⋅
c
o
s
(
π
2
n
+
1
)
oa_0=1, oa_n= oa_{n-1} \cdot cos\left( \dfrac{\pi}{2^{n+1}} \right)
o
a
0
=
1
,
o
a
n
=
o
a
n
−
1
⋅
cos
(
2
n
+
1
π
)
. Find
lim
n
→
+
∞
o
a
n
\lim\limits_{n\rightarrow+\infty} oa_n
n
→
+
∞
lim
o
a
n
.
Back to Problems
View on AoPS