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All-Russian Olympiad
1968 All Soviet Union Mathematical Olympiad
098
ASU 098 All Soviet Union MO 1968 2/(x^2-1)+..+20/(x^2-100)= ..
ASU 098 All Soviet Union MO 1968 2/(x^2-1)+..+20/(x^2-100)= ..
Source:
June 20, 2019
algebra
Problem Statement
Prove the equality
2
x
2
−
1
+
4
x
2
−
4
+
6
x
2
−
9
+
.
.
.
+
20
x
2
−
100
=
11
(
x
−
1
)
(
x
+
10
)
+
11
(
x
−
2
)
(
x
+
9
)
+
.
.
.
+
11
(
x
−
10
)
(
x
+
1
)
\frac{2}{x^2-1}+\frac{4}{x^2-4} +\frac{6}{x^2-9}+...+\frac{20}{x^2-100} =\frac{11}{(x-1)(x+10)}+\frac{11}{(x-2)(x+9)}+...+\frac{11}{(x-10)(x+1)}
x
2
−
1
2
+
x
2
−
4
4
+
x
2
−
9
6
+
...
+
x
2
−
100
20
=
(
x
−
1
)
(
x
+
10
)
11
+
(
x
−
2
)
(
x
+
9
)
11
+
...
+
(
x
−
10
)
(
x
+
1
)
11
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