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P3
Romania District MO 2022 Grade 12 P3
Romania District MO 2022 Grade 12 P3
Source: Romania District MO 2022 Grade 12
March 27, 2022
Integral
college contests
romania
Problem Statement
Find all values of
n
∈
N
∗
n\in\mathbb{N}^*
n
∈
N
∗
for which
I
n
:
=
∫
0
π
cos
(
x
)
⋅
cos
(
2
x
)
⋅
…
⋅
cos
(
n
x
)
d
x
=
0.
I_n:=\int_0^\pi\cos(x)\cdot\cos(2x)\cdot\ldots\cdot\cos(nx) \ dx=0.
I
n
:=
∫
0
π
cos
(
x
)
⋅
cos
(
2
x
)
⋅
…
⋅
cos
(
n
x
)
d
x
=
0.
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