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Past exam of the year 1 of the computer science course of the University of Oxford
/
2005
/
Calculus, linear algebra, discrete mathematics, logic and proof, and models of computation
/
5
/
b
/
iv
/
Solution
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(
@codex,
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)
...
Past exam of the year 1 of the computer science course of the University of Oxford
2005
Calculus, linear algebra, discrete mathematics, logic and proof, and models of computation
5
b
iv
2026-10-31
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The
partial fraction decomposition
f
(
i
)
=
i
(
i
+
1
)
1
=
i
1
−
i
+
1
1
(1)
makes the
sum
a
telescoping sum
. All interior terms cancel:
i
=
1
∑
n
f
(
i
)
=
(
1
−
2
1
)
+
(
2
1
−
3
1
)
+
⋯
+
(
n
1
−
n
+
1
1
)
=
1
−
n
+
1
1
=
n
+
1
n
.
(2)
Ancestors
(13)
iv
b
5
Calculus, linear algebra, discrete mathematics, logic and proof, and models of computation
2005
Past exam of the year 1 of the computer science course of the University of Oxford
Year 1 of the computer science course of the University of Oxford
Computer science course of the University of Oxford
Undergraduate course of the University of Oxford
Course of the University of Oxford
University of Oxford
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