The Fourier series of an odd periodic function, contains only

Odd harmonics
Even harmonics
Cosine terms
Sine terms

The correct answer is A. Odd harmonics.

A Fourier series is a way to represent a periodic function as a sum of sine and cosine waves of different frequencies. The frequencies of these waves are integer multiples of the fundamental frequency of the function.

An odd periodic function is a function that is symmetric about its midline, meaning that $f(-x) = -f(x)$ for all $x$. The Fourier series of an odd periodic function contains only odd harmonics, which are sine waves with frequencies that are odd multiples of the fundamental frequency.

For example, the function $f(x) = x$ is an odd periodic function with fundamental frequency $1$. The Fourier series of $f(x)$ is

$$f(x) = \frac{1}{2} + \frac{1}{2} \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n} \sin(n \pi x).$$

The first term in the Fourier series is a constant term, which represents the average value of $f(x)$. The other terms are sine waves with frequencies that are odd

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multiples of the fundamental frequency.

The Fourier series can be used to represent a wide variety of periodic functions. It is a powerful tool that can be used to analyze and understand periodic phenomena.

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