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Periodic functions/Rational ratio of lengths/Sum periodic/Exercise
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Let
f
1
,
f
2
:
R
⟶
R
{\displaystyle f_{1},f_{2}\colon \mathbb {R} \longrightarrow \mathbb {R} }
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.
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