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National and Regional Contests
Switzerland Contests
Switzerland Team Selection Test
2000 Switzerland Team Selection Test
14
14
Part of
2000 Switzerland Team Selection Test
Problems
(1)
P(k) = \frac{k}{k +1} , find P(n+1), polynomial
Source: Switzerland - Swiss TST 2000 p14
2/19/2020
The polynomial
P
P
P
of degree
n
n
n
satisfies
P
(
k
)
=
k
k
+
1
P(k) = \frac{k}{k +1}
P
(
k
)
=
k
+
1
k
for
k
=
0
,
1
,
2
,
.
.
.
,
n
k = 0,1,2,...,n
k
=
0
,
1
,
2
,
...
,
n
. Find
P
(
n
+
1
)
P(n+1)
P
(
n
+
1
)
.
polynomial
algebra