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Past exam of the mathematics course of the University of Cambridge
/
2025
/
iii
/
Paper 318
/
2
/
a
/
Solution
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Past exam of the mathematics course of the University of Cambridge
2025
iii
Paper 318
2
a
Created
2026-09-24
Updated
2026-09-25
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Substituting the
Fourier coefficient
s
into the
Fourier partial sum
and summing the
finite geometric series
gives
s
n
(
f
,
x
)
=
2
π
1
∫
T
f
(
t
)
∑
k
=
−
n
n
e
ik
(
x
−
t
)
d
t
=
π
1
∫
T
D
n
(
x
−
t
)
f
(
t
)
d
t
,
(1)
where
D
n
(
u
)
=
2
sin
(
u
/2
)
sin
((
n
+
2
1
)
u
)
.
(2)
Ancestors
(11)
a
2
Paper 318
iii
2025
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
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