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Canada National Olympiad
1975 Canada National Olympiad
2
Sequence
Sequence
Source:
July 27, 2008
induction
Problem Statement
A sequence of numbers
a
1
,
a
2
,
a
3
,
.
.
.
a_1, a_2, a_3, ...
a
1
,
a
2
,
a
3
,
...
satisfies (i) a_1 \equal{} \frac{1}{2} (ii) a_1\plus{}a_2 \plus{} \cdots \plus{} a_n \equal{} n^2 a_n \ (n \geq 1) Determine the value of
a
n
(
n
≥
1
)
a_n \ (n \geq 1)
a
n
(
n
≥
1
)
.
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