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## Homework Statement

Hi, my question is whether the sum and multiplication of two periodic functions (with a common period) are periodic.

Our functions are

**R**[itex]\rightarrow[/itex]

**R**.

## Homework Equations

## The Attempt at a Solution

f(x)=f(x+T) g(x)=g(x+T) T is the period.

h(x)=f(x)+g(x)

h(x+T)=f(x+T)+g(x+T)=f(x)+g(x)=h(x)

Hence, h(x) is also periodic.

What I did is similar for multiplication. Is there any flaw in this? I searched a bit and found out this may not hold every time, but I guess that was about Fourier series, which I have no idea about.

Thanks for any hint :)