IMO 1974 LL CZS9

Origin: CZS

Problem

Solve the following system of linear equations with unknown x1, . . . , xn (n \geq2) and parameters c1, . . . , cn: 2x1 −x2

c1; −x1 +2x2 −x3

c2; −x2 +2x3 −x4

c3; . . . . . . . . . . . . −xn−2 +2xn−1 −xn = cn−1; −xn−1 +2xn = cn.