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2002 IMC
3
sum equals zero
sum equals zero
Source: IMC 2002 day 1 problem 3
October 7, 2005
induction
algebra proposed
algebra
Problem Statement
Let
n
n
n
be a positive integer and let
a
k
=
1
(
n
k
)
,
b
k
=
2
k
−
n
,
(
k
=
1..
n
)
a_k = \dfrac{1}{\binom{n}{k}}, b_k = 2^{k-n},\ (k=1..n)
a
k
=
(
k
n
)
1
,
b
k
=
2
k
−
n
,
(
k
=
1..
n
)
. Show that
∑
k
=
1
n
a
k
−
b
k
k
=
0
\sum_{k=1}^n \dfrac{a_k-b_k}{k} = 0
∑
k
=
1
n
k
a
k
−
b
k
=
0
.
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