Home Competitions SE-SKOLORNAS 1983 Problem 3
SE-SKOLORNAS 1983 Problem 3
The systems of equations
{ 2 x 1 − x 2 = 1 − x 1 + 2 x 2 − x 3 = 1 − x 2 + 2 x 3 − x 4 = 1 − x 3 + 3 x 4 − x 5 = 1 ⋯ ⋯ ⋯ ⋯ − x n − 2 + 2 x n − 1 − x n = 1 − x n − 1 + 2 x n = 1 \left\{ \begin{array}{l}
2x_1 - x_2 = 1
-x_1 + 2x_2 - x_3 = 1
-x_2 + 2x_3 - x_4 = 1
-x_3 + 3x_4 - x_5 =1
\cdots\cdots\cdots\cdots
-x_{n-2} + 2x_{n-1} - x_n = 1
-x_{n-1} + 2x_n = 1
\end{array} \right. { 2 x 1 − x 2 = 1 − x 1 + 2 x 2 − x 3 = 1 − x 2 + 2 x 3 − x 4 = 1 − x 3 + 3 x 4 − x 5 = 1 ⋯⋯⋯⋯ − x n − 2 + 2 x n − 1 − x n = 1 − x n − 1 + 2 x n = 1 x i x_i x i n n n
Dataset text AI-MO AoPS . Quoted with source.
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