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APMO
2000 APMO
1
1
Part of
2000 APMO
Problems
(1)
Compute a sum
Source: APMO 2000
4/1/2006
Compute the sum:
∑
i
=
0
101
x
i
3
1
−
3
x
i
+
3
x
i
2
\sum_{i=0}^{101} \frac{x_i^3}{1-3x_i+3x_i^2}
∑
i
=
0
101
1
−
3
x
i
+
3
x
i
2
x
i
3
for
x
i
=
i
101
x_i=\frac{i}{101}
x
i
=
101
i
.
algebra unsolved
algebra