Let
be periodic functions with periods respectively L 1 {\displaystyle {}L_{1}} and L 2 {\displaystyle {}L_{2}} . The quotient L 1 / L 2 {\displaystyle {}L_{1}/L_{2}} is a rational number. Prove that f 1 + f 2 {\displaystyle {}f_{1}+f_{2}} is also a periodic function.